16PAT1 58 ตุลา
Transcript of 16PAT1 58 ตุลา
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PAT 1 (.. 58) 1
PAT 1 (..58) 71 (PAT 1)31 2558 13.00 -16.00.
1 1-30 6
1. , ~ ~ 1. 2. 3. 4. ~ 5. ~
2. , = , = 12 , = 15 , = 16 , = 20 = = 1.
= 10 2.
= 11 3.
= 4
4. ( )= 12 5. = 5
3.
| 1| 1 < 1 + + 1. (5, 1) 2. (3, 1) 3. (1, 3)4. (0, 4) 5. (1, 5)
5 Feb 2016
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2 PAT 1 (.. 58)
4. 3 4 s i n 93 4 s i n 273 4 s i n 813 4 s i n 243 1. 0 2. 1 3. 24. tan9 5. cot9
5. 2cot = 1 c o t 0 < < + 1. 0.125 2. 0.25 3. 14. 2 5. 4
6. secarctan2+ cosecarccot3+ cosec2arccot2arccos 1. 2. 3. 4.
5.
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PAT 1 (.. 58) 3
7. = arcsincos 0 < < sin + sin + sin5 1. 0 2. 1 3. sin24.
cos2
5.
2cos2
8.
2
log 2 = log 3+ log 2 (log )log = 1 + log + 1. 183 2. 210 3. 2164. 225 5. 239
9. 1. = , | 1 = 0 }2. = , | = tan }3.
=
,
=
1
4.
= , | = |2 |}5. = , = +
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4 PAT 1 (.. 58)
10. 6 1 2 = 0 > 0 4 3 = 71 14 = 7 1.
4 4 1 6 = 0 2.
4 4 1 6 = 0
3. 4 4 2 0 = 0 4. 4 8 4 4 = 05. 4 8 3 6 = 0
11.
4 4 0 2 3 6 = 0 (4, 6)
1. 4 9 8 3 6 1 4 0 = 0 2. 4 9 8 3 6 1 4 0 = 03. 4 9 8 3 6 1 4 0 = 0 4. 9 4 3 6 8 1 8 0 = 05. 9 4 3 6 8 1 8 0 = 0
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PAT 1 (.. 58) 5
12. 8 4 1 = 0 8 8 1 = 0 > 0
() [ ]
() [ ] () [ ]
1. () 2. () 3. () 4. () () () 5. () () ()
13. 1
limx
1 + 1. 0 2. 0.5 3. 1
4.
2
5.
4
14.
= 2 +
| 1|
(0, 2) (0, 2) 1. (1, 3) 2. (1, 5) 3. (2, 5)4. (3, 2) 5. (3, 4)
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6 PAT 1 (.. 58)
15. = +
() 24 4 = 3()
(4) =
(4)
() (0, 2)1. () () () 2. () () () 3. () () () 4. () () () 5. () () ()
16. = 16+ = 8+ = 60 1. 8 2. 16 3. 644. 192 5. 320
17. 4 4
1. 2. 3.
4. 5.
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PAT 1 (.. 58) 7
18. = {9 , 07 , > 4 = 2 , < 1 4 , 1
() 0 = 9 4()
4 < 6 = 3 () > 6 = 9
1. () () () 2. () () () 3. () () () 4. () () () 5. () () ()
19.
1 i + = 6 2i i= 1 (conjugate) () | 8| = 2() | 3 i| = 10() |i 2| = 8
1. () () () 2. () () () 3. () () () 4. () () ()
5.
() () ()
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8 PAT 1 (.. 58)
20. = = 1, 2, 3, 1n 1. 2. 43. 24 4.
5.
21. 1 + 4 , 4 , , + 42
2+ 4 ,
2
4 , , 2+ 4
, , , 1 501 102 1. 96 4002. 96 5763. 100 4004. 104 4005. 104 576
22. 25% 15.87 85 47.6
0
1. 34.46 2. 18.41 3. 13.574. 11.51 5. 9.68
0.4 0.9 1.0 1.1 1.2 1.3 0.1554 0.3159 0.3413 0.3643 0.3849 0.4032
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PAT 1 (.. 58) 9
23. = ++++ + = 1, 2, 3,
nlim
1. 2. 3. 4.
5.
24. = , = + + = | }1. 6 2. 10 3. 194. 29 5. 30
25. 2 4 , 1 , 1 , 0 01.
= 2
+ 2
2.
= 3
+ 2
3.
= 2
+ 3
4. = + 4 5. = 4+
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10 PAT 1 (.. 58)
26. = 1 22 1 = ,, = 9 = det= 24 1. 5 2. 6 3. 7
4. 8
5. 9
27. ()
=
||
()
= || () ||= 1. () () () 2. () () () 3. () () () 4. () () () 5. () () ()
28. ,, , 4 = 5 = 1 = 2 = 3
() < () < < <
() < 1. () 2. () 3. () 4. () () () 5. () () ()
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PAT 1 (.. 58) 11
29.
5 1. 3.8 2. 4.3 3. 4.84. 4.9 5.
30. 60
() 1.5 () ()
1. () 2. () 3. () 4. () () () 5. () () ()
0 2 33 5 56
8
9 11 3
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12 PAT 1 (.. 58)
2 31 -45 8 31.
150 80 60
30
32. 3 ( 9 3||+|+|)= 3|+| 3||+ = 59 | }
33. : 2
limx
+
+ = 6 1 +
0
6 = 4 = = 2 2
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PAT 1 (.. 58) 13
34. = , < 1 , 1 < 13 2 , 1
2
2
35. > 1 = log( ) = 1, 2, 3, = 77
36. 1 0 4 15
= 17 5 2 2 58 2 2 0
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14 PAT 1 (.. 58)
37. } = = 1275 = 200
38. 1, 2, 3
1 1 2 1 3 2
39. 8 () ()
8
1i
= 40 ,
8
1i
= 48 ,
8
1i
= 210 , 8
1i
= 380 , 8
1i
= 270
3 = < < < < 10 4
() : ()
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PAT 1 (.. 58) 15
40. = 21 2 1= 0 (asymtote) (1 + 25, 3)
41. (, ) , =
42. + + < 1
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16 PAT 1 (.. 58)
43. (, ) 2 = 2 3log 16= 6 + 6log = |, }
44.
5 , , , , 5
1i = 214
5
1i = 34 > 0
5 2, + 2, 2, 2, 2 16 , , , ,
45. = 143 , 1, 2, 3 , , 9}
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PAT 1 (.. 58) 17
1. 2 11. 3 21. 1 31. 230 ? 41. 4 ?2. 5 12. 3 22. 4 32. 126 ? 42. 1.5 ?3. 3 13. 1 23. 5 33. 5 ? 43. 2 ?4. 2 14. 1 24. 4 34. 9.25 ? 44. 78.7 ?
5. 5 15. 2 25. 5 35. 32 ? 45. 429 ?6. 4 16. 4 26. 4 36. 68 ?7. 4 17. 3 27. 3 37. - ?8. 2 18. 4 28. 1 38. 160 ?9. 3 19. 2 29. 2 ? 39. 3 ?10. 5 20. 3 30. 1 ? 40. 117 ?
1. 2
~ ~ ~ ~ T T T ~ ~ ~ T ~ F ~ F
F F ~ ~ ~ F ~ T ~ ~
F 1. 2.
3. 4.
5.
2.
2. 5
0
~
F F F
F
F F T F T F F F ~ ~ F T T T ~
F ~
T T T
T F
T T
= = =
0
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18 PAT 1 (.. 58)
= = ,, ,
= == = 12 Inclusive Exclusive
(1) (2) :
= 10 , = 1
1. 10 2. 11 3.
4. 12 5.
5.
0 = = = = = =
0
= + + + 20 = 12 + 15 + 16 + 20 = 43 + 2+ 3 = 23 2
0 + + + = 12+ 2 = 12 1
2 = 12 12+ 3 = 23 22 (1) : 2 4 = 24 3(3) (2) : = 1 (1) : 21 = 12 = 10
0 1
1 110 = 15
= 16
0 1
1 110
3
4
0 1
1 110
3
4
0 1
1 110
3
4
= = 4
0 1
1 110
3
4
0 1
1 110
3
4
= =
4
0 1
1 110
3
4
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PAT 1 (.. 58) 19
3. 3: | 1| 1 < 1
0 < | 1| | 1| < 2
: (1, 3) 3
(
1, 3)
(
1, 3)
3 ( ) :
1
(1, 3) 3
4.
2 sin3= 3sin 4sin sin sin3
=( ) ( ) ( ) ( )
=
=
=
729 360 9 = = 1
1< | 1| 1 < 10 2
= |2 |= | 2| (2, 0)
= = + = + = =
+ 1 = 0 = 1
= + = +
1
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PAT 1 (.. 58) 23
10. 5
, 3 )
, 3 ++ = || = 14
> 0 = 4 (*) , 3= (2, 3) F(2, 3) = 7 V F V(
2,
+
) = V(
2, 5
=
2
= 5
= 5 3 = 2
11. 3
= 4 V(, ) = (6, 2) = = 10 F(610, 2)= F(4, 2)
6 1 2 = 0 + 6 = 12
6 3 =
1 2
3
+ 3 = 21 +
2
=
4 3 = 714 3 7 1 = 0
(, ) = 0 |++|+
|| = 14|262| = 70262 = 70 , 702 = 132 , 8 = 66, 4
= 4 ( 2) = 42 5 2 = 8 5 4 4 = 840 4 8 3 6 = 0
F(2, 3)= 7
V(
,
)
4 =
40+ 236
4 4 = 40+ 236 + 4 2 = 40240 2 = 40 6 2 = 410 6V(6, 2)
F
10
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24 PAT 1 (.. 58)
F(6, 2) F(4, 2)
(, ) = ( + , 2 ) = (1, 2) = 6 1= 5 A AF+ AF = A(4, 6) A F(6, 2) F(4, 2)
= 65 = = 35
12. 3 1. [ ] 8 4 1 +1 8
=
AF+ AF = 4 6 6 2+ 44 6 2 = 4 16 + 64 16=
20 +
80
=
25 +
45 =
65
F
= 5F
(1, 2) (6, 2)(4, 2)
= (35) = 545 = + 2520 = + = 1() + = 1+ + + = 1(+)+(+)
= 1
4 8 4 9 3 6 3 6 = 1804 9 8 3 6 1 4 0 = 0
8 4 1 = 08 1 1 4 1 = 08 1 4 2 = 02 1 22 1 = 02 14 2 1 22 1 = 02 14 2 1 2 = 02 14 2 1 = 0
1 1 =
= = =
=
2+ 1
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PAT 1 (.. 58) 25
= 8 8 1 = 2 1= 1 0
1. 2. [ ] 1 1
= 1 ,
=
1 :
1
1 =
1 1
= 0
0
= 1 2.3. [ ] 1. = = : = > 0 3. 13. 1
1
+
=
++
= ++ +
= 1 1 1 2 1 ++ + = (
) + = () +
=()() +
= ()+
= 1 ()+ = = 0
8 8 1 = 08 1 1 = 08 1 1 1 = 0 18 1 1 = 0 18 8 1 = 0 18 1 1 8 1 = 0
18
1 8
2 = 0
1(8 1 24 1) = 0 1(2 14 2 1 22 12 1) = 0 12 1(4 2 1 22 1) = 0 12 14 2 1 4 2 = 0 12 14 2 1 = 0
1 1
= =
+ 1 =
= 1 2 1
=
1 2 1 0 12 1 12 1 1 0 1
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26 PAT 1 (.. 58)
14. 1 = 2 + | 1| (0, 2) (0, 2) 0 1 | 1|= 1 (0, 2)
(0, 2) = 0 2 1 0, 2 = 0 = 0 20 1 = 1 = 1 1 = 1 ( 1 1 = 1) (0, 2) = = 1
= 21. 1+ 3 = 2 2. 1 5 2 3. 2 5 24. 3 + (2 2 5. 3 + 4 2
1. 15. 2() = 4
=
+
=
+
= ) =
() 4 = = 2 () 4 = = () () = 2 2 = 4 2 2
= 4 2 1= )
(4) =2 = = (4) = = =
=
=
|| = 0 < 0= 2 +
( 1)
= 2
2 =
= 2
=
=
+
= 2 2 = 2 = =
= =
)
=
24 4= 2 2= 3 ()
()
()
()
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PAT 1 (.. 58) 27
() () = 2 (= 2 ) 0, 2 () 16.
4
= |16+ | = |8+ |
() = 0: = 2:
= 0 = 192 = 0 (192) = (192) = 19217. 3 8 = 8! = + = +
1 : 4 4! 2 : 5
1 5 2 4 ( )3 3 4 2
= 4! 5 4 3 2 = 4! 5! 4
= 4! 5!
= cos16 8 = cos60(16)(8) + =
128 +
=
16
256 + 2 = 256 + 0 = 20 = 2 = 0 = 2
= 60
16 = 8 256 + = 64 + )
256 + 0 = 64 + 192 = 192 =
256 + 2 = 64 + 256 + 4 = 64 + 3 = 192 (3)
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28 PAT 1 (.. 58)
1 : 8 2 : 2 4
3 : 3 2
1 3 8 4 3 3 2 2 1 1 = 8 4! 3!
= 2(4! 5!) 8 4! 3! = ! ! !!! = ! ! = = 18. 4
() 0 = 9 = () = (9 ) 0
() 4 < 6 = 7
=
() =
7
4 < 6
() > 6 = 7 = () = 7
> 6
19. 2 = i = i
09 99 3 (9 ) = 4 (9 ) = 9 4 ()
4 > 67 4 > 7 7 63 > 7 1 7 = 4 7 = 7 4 = 3 ()