รายงานสถิติการขนส ง ประจําป 2561...รถยนต น งไม เก น 7 คน 9,362,259 ค น24.47% รถยนต น งเก
ภาคการศึกษา ภาคต น /2563...ต วอย างท 2 น กศ...
Transcript of ภาคการศึกษา ภาคต น /2563...ต วอย างท 2 น กศ...
มหาวทยาลยสโขทยธรรมาธราช
กจกรรมประจาชดวชา
97210 คณตศาสตรประยกตสาหรบเทคโนโลยอตสาหกรรม ภาคการศกษา ภาคตน/2563
สาขาวชาวทยาศาสตรและเทคโนโลย
2
คานา
เนองดวยมหาวทยาลยสโขทยธรรมาธราช มงใหผเรยนและนกศกษาไดมสวนรวมในกระบวนการศกษา
เลาเรยนครบวงจร ตงแตกอนเรยน ระหวางเรยน และหลงจากเรยนเสรจสนไปแลว โดยจดระบบการประเมนครบ
สวน ทงการประเมนกอนเรยน ระหวางเรยน และประเมนผลสดทาย
การประเมนกจกรรม เปนสวนหนงของการวดผลสมฤทธทางการเรยนสดทาย จงใหผเรยนและ
นกศกษาทากจกรรมภาคปฏบตตามทกาหนดใหโดยมวตถประสงคเพอใหผเรยนและนกศกษามความสามารถ ดงน
1. สรปหรอประมวลเนอหาสาระของเอกสารการสอนทงชดวชาหรอกลมเนอหากลมใดกลมหนง
2. ประยกตความรจากเอกสารการสอนเพอจดทาโครงการพฒนางานอยางใดอยางหนง ท
นกศกษาทา
3. พฒนาระบบ โครงการ ชนงาน ฯลฯ ตามกระบวนการหรอขนตอนทแสดงไวในหนวยใดหนวย
หนงของเอกสารการสอน
4. คด วเคราะห นาเสนอขอมลและความคดในเชงสรางสรรค
นอกจากนการทากจกรรมประจาชดวชายงทาใหนกศกษาไดศกษาเอกสารการสอนตงแตตนภาค
การศกษา และจากการวจยพบวานกศกษาททากจกรรมจะมโอกาสสอบผานในปลายภาคมากกวานกศกษาทไมทา
กจกรรม
คณะกรรมการบรหารชดวชาความรทวไปเกยวกบการพมพขอใหนกศกษาทกทานประสบความสาเรจ
ในการศกษาชดวชาน และสามารถนาความรไปเปนประโยชนตอการดาเนนชวต และการทางานสบไป
คณะกรรมการบรหารชดวชา
97210 คณตศาสตรประยกตสาหรบเทคโนโลยอตสาหกรรม
1 สงหาคม 63
3
เกณฑการใหคะแนนกจกรรมจะพจารณาจากการตอบทตรงประเดนคาถาม การครอบคลมความถกตอง
ของคาตอบ ความชดเจนของการนาเสนอ ความละเอยดประณตของชนงาน
มหาวทยาลยไมบงคบใหนกศกษาทกคนตองทากจกรรม นกศกษาอาจเลอกทาหรอไมทากได โดยการ
ประเมนปลายภาคสาหรบชดวชาน แบงออกเปน 2 กรณ
กรณท 1 นกศกษาทากจกรรม มหาวทยาลยจะแบงคะแนนออกเปน 2 สวน สวนแรกจากคะแนนสอบ
ปลายภาคคดรอยละ 80 และสวนทสองจากคะแนนกจกรรมรอยละ 20 และคะแนนกจกรรมจะนาไปใชทงการ
ประเมนผลสอบไลและสอบซอม นกศกษาทมไดสงกจกรรมในการสอบไลจะสงกจกรรมเพอเปนคะแนนในการสอบซอม
ไมได
กรณท 2 นกศกษาไมทากจกรรม มหาวทยาลยจะประเมนผลจากการสอบปลายภาคเพยงอยางเดยว
ในการประเมนผลปลายภาค นกศกษากลมททากจกรรมและไมทากจกรรมจะตองประเมนผลโดยใช
ขอสอบฉบบเดยวกน นกศกษากลมททากจกรรมมคะแนนเตม 80 คะแนน สวนนกศกษากลมทไมทากจกรรมจะม
คะแนนเตม 100 คะแนน สาหรบนกศกษาททากจกรรม มหาวทยาลยจะพจารณาใหนกศกษาไดประโยชนสงสด โดย
การนาคะแนนสอบปลายภาคของนกศกษาเพยงอยางเดยวมาเปรยบเทยบกบการคดคะแนนสอบปลายภาครวมกบ
คะแนนกจกรรม แลวนาคะแนนสวนทมากกวาไปใชในการตดสนผลการสอบใหกบนกศกษา ดงตวอยางตอไปน
ตวอยางท 1 นกศกษาไดคะแนนกจกรรม 18 คะแนน และทาขอสอบได 70 ขอ (คดเปน 70 x 0.66666
เทากบ 46.67 คะแนน) นกศกษาจะไดคะแนนกจกรรมรวมกบคะแนนสอบปลายภาค 18 + 46.67 เทากบ 64.67
คะแนน กรณคดคะแนนจากการสอบปลายภาคเพยงอยางเดยว นกศกษาจะได 70 x 0.83333 เทากบ 58.33 คะแนน
มหาวทยาลยจะเลอกใหนกศกษาไดคะแนน 64.67 คะแนน
ตวอยางท 2 นกศกษาไดคะแนนกจกรรม 13 คะแนน และทาขอสอบได 92 ขอ (คดเปน 92 x 0.66666
เทากบ 61.33 คะแนน) นกศกษาจะไดคะแนนกจกรรมรวมกบคะแนนสอบปลายภาค 13 + 61.00 เทากบ 74.33
คะแนน กรณคดคะแนนจากการสอบปลายภาคเพยงอยางเดยว นกศกษาจะได 92 x 0.83333 เทากบ 76.67 คะแนน
มหาวทยาลยจะเลอกใหนกศกษาได 76.67 คะแนน
1. การประเมนผล
4
ใหนกศกษาดาเนนการดงน
1. กรอกขอมลและระบายรหสประจาตวนกศกษา รหสชดวชา รหสจงหวดใหครบถวนดวยดนสอ2B ลง
ในแบบกรอกคะแนน (สสม) ตามตวอยางในแบบกรอกคะแนน
2. ใหนกศกษาระมดระว งอย าใหแบบกรอกคะแนนฉกขาด ในกรณท ทาแบบกรอกคะแนน
ฉกขาดหรอสญหาย ใหนกศกษาเขยนชแจงมาพรอมกบกจกรรมทสงไปยงมหาวทยาลย โดยไมตอง
ถายเอกสารเพราะเครองอานจะไมอานเอกสารทมาจากเครองถายเอกสาร
3. ใหนกศกษาสงกจกรรมประจาชดวชาฉบบจรงไปยงมหาวทยาลยและสาเนากจกรรมททาเสรจแลวไว
1 ชด ไวเปนหลกฐาน
4. การสงกจกรรมประจาชดวชาภายในวนท 30 ตลาคม 2563
5. ใหจดทาหนาปกรายงานใหมขอความตามตวอยางทแนบมา
6. สงกจกรรมททาเสรจเรยบรอยแลวพรอมแบบกรอกคะแนนดวยตนเอง ณ สานกบรการการศกษา
มหาวทยาลยสโขทยธรรมาธราช หรอสงทางไปรษณยลงทะเบยน โดยจาหนาซองดงน
ในกรณทสงทางไปรษณยใหเกบสลปหรอตนขวการสง และถายเอกสารกจกรรมทสงไปมหาวทยาลยไว
เปนหลกฐาน ในการสงกจกรรมทกชน นกศกษาจะตองจดทาหนาปกรายงาน (ปรากฏในภาคผนวกทสงมาดวย)
7. นกศกษาสามารถตรวจสอบวาสานกบรการการศกษาไดรบกจกรรมทนกศกษาสงไปแลวหรอยง โดยโทรศพท
สอบถามหมายเลข 0-2982-9633 หรอโทรศพทตดตอสานกบรการการศกษา หมายเลข 0-2-504-7621 หรอ โทรศพท
ตดตอศนยสารสนเทศ หมายเลข 0-2503-3545-8 และ หมายเลข 0-2504-7191,0-2504-7193 โ ท ร ส า ร 0-2503-
3546 โทรศพทฝากขอความนอกวน-เวลาราชการ (ตลอด 24 ชวโมง) หมายเลข 0-2504-7191, 0-2504-7191 E-
mail : [email protected]
2. การสงกจกรรมประจาชดวชา
ศนยบรการการสอนทางไปรษณย
สานกบรการการศกษา
มหาวทยาลยสโขทยธรรมาธราช
ตาบลบางพด อาเภอปากเกรด
จงหวดนนทบร 11120
(กจกรรมประจาชดวชา 97210 คณตศาสตรประยกตสาหรบเทคโนโลย
อตสาหกรรม
สาขาวชาวทยาศาสตรและเทคโนโลย)
5
∀
ปกรายงาน
กจกรรมประจาชดวชา
97210 คณตศาสตรประยกตสาหรบเทคโนโลยอตสาหกรรม
ภาคการศกษาท ภาคตน/2562
สาขาวชาวทยาศาสตรและเทคโนโลย
ชอนกศกษา………………………………………………………………………….
รหสประจาตวนกศกษา
ทอย …………………………………………………………….………………………………
……………………………………………………………………………...........................
โทรศพท (ถาม) …………………………………………………………….
ขาพเจาขอยอมรบการตดสนผลคะแนนภาคปฏบตจากผประเมนเปนทสด
ลงชอ…………………………………………….
(………………………………………………)
∀
6
กจกรรมประจาชดวชา 97210 คณตศาสตรประยกตสาหรบเทคโนโลยอตสาหกรรม คะแนนเตม 75
คะแนน คดเปน 20 คะแนน ใหนกศกษาตอบคาถามตอไปนทกขอใหครบถวนและตรงประเดน โดยการพมพ
หรอเขยนดวยลายมอตนเองเปนลายมอทอานงาย
หนวยท 1 (5 คะแนน)
ขอ 1 จงวเคราะหหาคา 𝐥𝐥𝐥𝐥𝐥𝐥 𝒙𝒙→𝟐𝟐
(𝒙𝒙𝟐𝟐+𝒙𝒙−𝟔𝟔)(𝟐𝟐𝒙𝒙+𝟑𝟑)(𝒙𝒙−𝟐𝟐)
คาแนะนา ใชหลกการพจารณาความตอเนองของฟงกชน และ การแยกตวประกอบ และสมบตการหารของพหนาม
(ตอบใหสมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
............................................................................................................................................. ..............................................
3. เนอหากจกรรม
คะแนน
7
หนวยท 2 (5 คะแนน)
ขอ 2 จงวเคราะหหาคาอนพนธของ 𝒇𝒇(𝒙𝒙) = �𝒙𝒙𝟐𝟐+𝟑𝟑𝟑𝟑𝒆𝒆𝒙𝒙
คาแนะนาใชกฏลกโซ การหาอนพนธของผลหาร และการหาอนพนธของฟงกชนอดสย (ตอบใหสมบรณภายในพนท
เขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
................................................................................................................................................................................. ..........
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
8
หนวยท 3 (5 คะแนน)
ขอ 3 จงวเคราะหหาคาปรพนธตอเนองบนชวงของ ∫ (𝟐𝟐𝒙𝒙𝟑𝟑 + 𝟒𝟒𝒙𝒙𝟐𝟐 − 𝒙𝒙 + 𝟏𝟏)𝒅𝒅𝒙𝒙𝟑𝟑𝟎𝟎
(ตอบใหสมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
......................................................................................................................................................................... ..................
........................................................................................................... ................................................................................
คะแนน
9
หนวยท 4 (5 คะแนน)
ขอ 4 จงวเคราะหหาคาปรพนธทละสวนของ ∫𝟑𝟑𝒙𝒙𝒆𝒆𝟑𝟑𝒙𝒙𝒅𝒅𝒙𝒙
(ตอบใหสมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
......................................................................................................................................................................... ..................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
10
หนวยท 5 (5 คะแนน)
ขอ 5 จงวเคราะหหาพนทปดลอมดวยเสนโคงพาราโบลา 𝟒𝟒𝟒𝟒 − 𝟒𝟒𝟐𝟐 = 𝒙𝒙
คาแนะนา ให วาดภาพพาราโบลา ซงเปน พาราโบลาตะแคงซาย คาลไปทางซาย จดยอดอยท (4,2) ตดแกน y ท (0,0)
และ (0,4)
(ตอบใหสมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
......................................................................................................................................................................... ..................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
......................................................................................................................................................................... ..................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
11
หนวยท 6 (5 คะแนน)
ขอ 6 จงวเคราะหหาพจนทวไปของลาดบ 𝟏𝟏𝟏𝟏∙𝟒𝟒
,− 𝟏𝟏𝟑𝟑∙𝟖𝟖
, 𝟏𝟏𝟓𝟓∙𝟏𝟏𝟐𝟐
,− 𝟏𝟏𝟕𝟕∙𝟏𝟏𝟔𝟔
, …
(ตอบใหสมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
............................................................................................................................................. ..............................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
12
หนวยท 7 (5 คะแนน)
ขอ 7 จงวเคราะหหาคา 𝐥𝐥𝐥𝐥𝐥𝐥(𝒙𝒙,𝟒𝟒)→(𝟐𝟐,−𝟏𝟏/𝟐𝟐)
(𝒙𝒙−𝟒𝟒)𝟑𝟑(𝒙𝒙−𝟐𝟐)𝟐𝟐(𝟐𝟐𝟒𝟒+𝟏𝟏)(𝒙𝒙−𝟐𝟐)(𝟐𝟐𝟒𝟒+𝟏𝟏)
(ตอบใหสมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
......................................................................................................................................................................... ..................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
13
หนวยท 8 (5 คะแนน)
ขอ 8 กาหนดให 𝒇𝒇(𝒙𝒙,𝟒𝟒) = 𝟓𝟓𝒙𝒙𝟓𝟓𝟒𝟒(𝒙𝒙+𝟒𝟒𝟐𝟐)𝟐𝟐
จงวเคราะหหาคา 𝝏𝝏𝒇𝒇𝝏𝝏𝒙𝒙
และ 𝛛𝛛𝒇𝒇𝛛𝛛𝛛𝛛
(ตอบใหสมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
......................................................................................................................................................................... ..................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
14
หนวยท 9 (5 คะแนน)
ขอ 9 จงวเคราะหหาคา เวกเตอรสมผส 𝑻𝑻�� (𝒕𝒕) และ เวกเตอรแนวฉากหนงหนวย 𝑵𝑵�� (𝒕𝒕) ของเสนโคง 𝒓𝒓� (𝒕𝒕) =
𝟐𝟐𝒕𝒕𝒊𝒊 − 𝟒𝟒𝒕𝒕𝟐𝟐𝒋𝒋 − 𝟏𝟏𝟎𝟎𝒕𝒕𝒌𝒌�� , 𝒕𝒕 > 𝟎𝟎
(ตอบใหสมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
............................................................................................................................................. ..............................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
......................................................................................................................................................................................... ..
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
15
หนวยท 10 (5 คะแนน)
ขอ 10 จงวเคราะหหาคาปรพนธรอบพนท R คอ ∭ 𝒇𝒇(𝒙𝒙,𝟒𝟒, 𝒛𝒛)𝒅𝒅𝒛𝒛𝒅𝒅𝟒𝟒𝒅𝒅𝒙𝒙 𝑹𝑹 เมอ 𝒇𝒇(𝒙𝒙,𝟒𝟒, 𝒛𝒛) = 𝟐𝟐𝟒𝟒𝒛𝒛
และ R เปนรปสเหลยมมมฉาก โดยท 𝑹𝑹 = {(𝒙𝒙,𝟒𝟒, 𝒛𝒛)| − 𝟐𝟐 ≤ 𝒙𝒙 ≤ 𝟐𝟐,−𝟏𝟏 ≤ 𝟒𝟒 ≤ 𝟐𝟐, 𝟎𝟎 ≤ 𝒛𝒛 ≤
𝟓𝟓}
(ตอบใหสมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
......................................................................................................................................................................... ..................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
16
หนวยท 11 (5 คะแนน)
ขอ 11 จงวเคราะหหาจาโคเบยนของการแปลงตวแปร x,y ไปเปนตวแปร u,v เพอหาคาปรพนธสองชนของ 𝒙𝒙 =𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐, 𝟒𝟒 = 𝟐𝟐𝒆𝒆𝟑𝟑𝟐𝟐 (ตอบใหสมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
....................................................................................... ....................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
......................................................................................................................................................................... ..................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
17
หนวยท 12 (5 คะแนน)
ขอ 12 จงวเคราะหหาผลเฉลยของสมการเชงอนพนธ 𝟒𝟒′ + 𝟒𝟒𝒙𝒙
= 𝒆𝒆𝟐𝟐𝒙𝒙
𝟒𝟒𝒙𝒙 (ตอบใหสมบรณภายในพนทเขยนท
กาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
......................................................................................................................................................................... ..................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
18
หนวยท 13 (5 คะแนน)
ขอ 13 จงวเคราะหหาผลเฉลยทวไปของสมการเชงอนพนธ 𝟐𝟐 𝒅𝒅𝟐𝟐𝟒𝟒𝒅𝒅𝒙𝒙
− 𝟖𝟖 𝒅𝒅𝟒𝟒𝒅𝒅𝒙𝒙
+ 𝟏𝟏𝟎𝟎𝟒𝟒 = 𝟏𝟏𝟎𝟎𝒆𝒆𝒙𝒙(ตอบให
สมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
......................................................................................................................................................................... ..................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
19
หนวยท 14 (5 คะแนน)
ขอ 14 จงหาอนกรมฟเรยรของ 𝒇𝒇(𝒙𝒙) = 𝟐𝟐𝒙𝒙𝟐𝟐 + 𝟏𝟏 เมอ -3 < x < 3 และ 𝒇𝒇(𝒙𝒙 + 𝟒𝟒) = 𝒇𝒇(𝒙𝒙) (ตอบให
สมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
......................................................................................................................................................................... ..................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
คะแนน
20
หนวยท 15 (5 คะแนน)
ขอ 15 จงหารากทเปนบวกของสมการพนนาม 𝒙𝒙𝟐𝟐 − 𝟒𝟒𝒙𝒙 + 𝟒𝟒 = 𝟎𝟎 โดยวธแบงครงชวงโดยกาหนดใหคาขอบ
ซาย (xL) และคาขอบขวา (xR) เรมตนเปน 0 และ 1 ตามลาดบ โดยแสดงการคานวนในรปแบบตาราง (ตอบให
สมบรณภายในพนทเขยนทกาหนดให 1 หนากระดาษเทานน)
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
......................................................................................................................................................................... ..................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
........................................................................................................... ................................................................................
......................................................................................................................................................................... ..................
คะแนน
21
ใหนกศกษาตอบคาถามประเมนการจดการเรยนการสอนชดวชาวสดทางการพมพและบรรจภณฑ
โดยตอบในแบบกรอกน
1. กจกรรมประจาชดวชานชวยใหนกศกษามความเขาใจเนอหาในเอกสารการสอนมากขน
เหนดวย
ไมเหนดวย โปรดระบเหตผล
...............................................................................................................................................................................................
...............................................................................................................................................................
2. นกศกษาคดวาคาถามโดยรวมทปรากฏอยในกจกรรมประจาชดวชาน มความยากมากนอยเพยงใด โดยระบเปน 5
ระดบ ดงน
นอยทสด นอย ปานกลาง มาก มากทสด
3. นกศกษาคดวาคาถามขอใดทควรปรบปรง โปรดระบเหตผล
...............................................................................................................................................................................
...............................................................................................................................................................................
...............................................................................................................................................................................
4. ความพงพอใจโดยรวมของการจดการเรยนการสอนของชดวชาน มากนอยเพยงใด โดยระบเปน 5 ระดบ ดงน
นอยทสด นอย ปานกลาง มาก มากทสด
5. นกศกษาคดวาการจดการเรยนการสอนในชดวชานควรปรบปรงในเรองใด โปรดระบ
เอกสารการสอน
แบบฝกปฏบตชดวชา
ดวด
กจกรรมประจาชดวชา
อนๆ โปรดระบ
ขอบคณทใหขอมล
4. ประเมนการจดการเรยนการสอน