m1_zadvj(1)
of 10
Transcript of m1_zadvj(1)
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f(x) =
x1x2
f(x) =
x+
x+ 1
f(x) =
x
x+ 1
f(x) =
x+1x
f(x) =
x(x+ 1)
f(x) =
2x
f(x) =x
x4
f(x) =
(x 2)(x 4)
f(x) =
x 2 x 4
f(x) =
x 2 + x 4
f(x) =
(x1)(x2)(x+1)(x+2)
f(x) =
x
(x+2)(x+3)
x2+1x+2
f(x) =
x2x+1x+3
Df =, 1] 2, Df = [0, Df = [0, Df =0, Df = [, 1][0, Df = [0, Df =4, Df =[, 2] [4, Df = [4, Df = [4, Df =, 2 1, 1] [2,
Df = [0, Df = [0,
R
|x|= 2
|x|=3
|x+ 1|= 4
|x| + |x+ 1|= 5
x2 + 5x+ 4
+ |x 3|= 1
x+ |x+ 2| = x+ 2
x+x+ |x+ 1|
= 7
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|x| 7
|x 2|< 6
|x+ 1| + |x+ 2| + |x+ 3|> 3
x |x+ 1|
< 3
2x+ |1 x| 5
x {2, 2} x {5, 3} x {3, 2} x 43 , 0 x {8, 2} x , 7][7, x 4, 8 x , 3 1,
x 2,
x , 6] [2,
2x 0.5 3x = 4
2x 3 1x 16 = 0
4x + 6x = 2 9x
4 25x + 5 16x = 9 20x
71|x| = 49
31+|x+1| = 9
32
3|3x4| = 92x3
9x2
22x1 = 8
4x+2 32x+1 = 8 6x1
3x+1 4 3x1 = 45
5x + 3 5x2 = 140
32x1 + 32x2 32x4 = 315
3x + 3x+1 + 3x+2 = 25
4x
2x+3 + 15 = 0
9x 3x+1 = 4
4x1 2x1 = 12
7 6x 62x = 6
4x + 6x = 2 9x
x {1, 3}
x {1, 3}
x = 0
x {0, 1}
x {
3, 1}
x = 2 x = 2 x =
2 x = 3 x = 3 x = 3
x= log32513 x {log23, log25} x= log34 x= 3 x {0, 1} x= 0
ln(x 1) + ln(x 2) = 2ln(x 3)
log x+ log(x 3) = 1
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ln(x 2) + ln(x+ 2) = 2 ln(x 1)
log2 x+ 2 log x10 = 1
log2(100x) + log2(10x) = 14 + log 1
x
log x
2
10 log 10x =3
log3log8log2x= log32 1
log(3 + 2 log(x+ 1)) = 0
log4x+ log8x= 5
log2x log 12 x= 8
log16x+ log8x+ log2x= 1936
log3x log9x log27x= 43
2log3log2x= log3(3 2log2x)
log4log2x+ log2log4x= 2
x = 5
x = 52 x
11000 , 10
x
1092 , 10
x
110
, 100
x= 16
x= 910 x= 64 x= 16 x= 8 x= 9
x= 2
x= 16
cos
2x 3
=
32
sin
x
2 +
6
=1
sin4x+ sin x= 0
cos2x= cos x
cos2t 5sin t 3 = 0
sin2 x+ 3 sin x cos x+ 2 cos2 x= 0
6sin2 x+ sin x cos x cos2 x= 2
2sin x 3cos x= 1.
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cos
2x
3 1
| sin x| 1
2
| cos x| 1
2
ctg x1
|tg x| 3
x 712 +k : kZ4 +k : kZ x 43 + 4k : kZ
x
2k5 :k
Z
3 +
2k3 :k
Z x
2k3 :k
Z {
2k : k
Z
} =
2k3
:kZ
cos2t= 12sin2 t
t 6
+ 2k : kZ56
+ 2k : kZ
x {arctg(2) +k : kZ}4 +k : kZ 2 = 2 cos2 x+ sin2 x x 4 +k : kZarctg 34 + k : kZ x 2arctg 1 3 + 2k : kZ x
kZ712 +k,
34 +k
x R\ 43 + 4k : kZ
xkZ
4 + 2k, 4 + 2k kZ 34 + 2k, 54 + 2k= kZ 4 +k, 4 +k
xkZ
k, 4 +k
xkZ
3 +k , 3 +k
f(x) = x5 4x3 + 2x 3
f(x) = ax
6+ba2+b2
f(x) =
x
f(x) = 3x23 2x52 +x3
f(x) = a3x2
bx3x
f(x) = 2x+3x25x+5
f(x) = 22x1 1x
f(x) = sinx+cosxsinxcosx
f(x) = arctg x+ arcctg x
f(x) = ex arcsin x
f(x) = tg x ctg x
f(x) = x
2
lnx
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f(x) = 2x arcsin x
f(x) = x
2
chx
h(x) =ax+bc
3
h(x) = 12x1
h(x) =esin2x
h(x) =
ctg x
h(x) = 1 + arcsin x h(x) =
xex +x
h(x) = 3
2ex 2x + 1 + (ln x)5
h(x) = arcsin 1x2
h(x) = 15x
2
h(x) = log sin x
h(x) = ln (ex + 5 sin x 6 arcsin x) h(x) = 2x2 2x+ 1 1
x
h(x) =a+bxn
abxnn
h(x) = 3
x+
x
h(x) = ln
1 +ex 1 ln 1 +ex + 1
h(x) =
ex, R
h(x) = ln (x2)5
(x+1)3
h(x) = ln ln
3 2x2
h(x) = 2arcsin3x + (1arccos3x)2
2
h(x) = arctg ln x.
f(x) = (sin x)cosx
f(x) = x1x
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f(x) = x+xx +xxx
f(x) =
1 + 1x
x
f(x) = 5x4 12x2 + 2
f(x) = 6ax5
a2+b2
f(x) = 12x
f(x) = 23x 5x32 3
x4 f(x) = 23ax
53 + 43bx
73
f(x) = 2x26x+25
(x25x+5)2
f(x) = 4(2x1)2 +
1x2
f(x) = 2(sinxcosx)2 f
(x) = 0
f(x) =
ex
11x2
+ arcsin x
f(x) = 1cos2 x
+ 1sin2 x
f(x) =x 2lnx
1ln2 x
f(x) =
2x
ln 2 arcsin x+ 11x2
f(x) = 2xchxx2shx
ch2x
h(x) = 3ax+bc
2 ac
h(x) = 2(2x1)2 h
(x) = esin2 x sin2x
h(x) = 12ctgx
1sin2 x
h(x) =
121+arcsinx
11x2
h(x) = ex+xex+12xex+x
h(x) = 13(2ex 2x + 1) 23 (2ex 2x ln2)+
5 ln4 xx
h(x) = 2xx41
h(x) =2 l n 5x5x2
h(x) = ctgxln10 h(x) =
ex+5cosx 61x2
ex+5sin x6 arcsin x h(x) = x1
x2
2x22x+1
h(x) = na+bxn
abxnn1
2abnxn1(abxn)2
h(x) = 13
(x+
x) 2
3
1 + 1
2x
h(x) = 1
1+ex h(x) =
2ex
2 h(x) =
2x+11(x+1)(x2) h
(x) = 4x(2x23) ln(32x2)
h(x) = 319x2
2arcsin3x ln2 + 1 arccos 3x
h(x) = 1x(1+ln2 x)
f(x) = (sin x)cosx( sin x ln sinx + ctg x cos x) f(x) = x
1x2(1ln x) f(x) = 1 + xx(ln x + 1) + xxxxx(ln x+ 1)ln x+xx1
f(x) =
1 + 1x
x ln 1 + 1x
1x+1
.
K . . . y= x3
3
1
K1. . . 2y= x2
K2. . . 2y= 8 +x2 + 2x.
P. . . y= x2 +ax+b a b P y = x x = 2
y = (x+ 1) 3
3 x
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T1(1, 0) T2(2, 3)
y= 4x x2
x
y= x2 + 4x
x
y = x2
2x+ 5
y= x2x
1
y= 3x4 + 4x3 12x2 + 20
y = x2 7x+ 3
5x+y 3 = 0 ?
y= (x 1)(x 2)(x 3)
P. . . y = x2 4x+ 5
P
P y
t . . . y = x+ 23
n . . . y =x 43 y =4x8. a =3 b = 4 n . . . y =x + 4 T1 : t . . . y = 3
4x + 3
4, n . . . y = 134x
134
T2 : t . . . y = 3, n . . . x = 2 (0, 0) : t . . . y = 4x. (4, 0) : t . . . y =4x+ 16.
(2, 4)
12 ,
174
y = 2x 1
(0, 20), (2, 12), (1, 15). (1, 3) (1, 0) : t . . . y = 2x 2, n . . . y =12x+ 12 . (2, 0) : t . . . y =x+ 2, n . . . y = x 2. (3, 0) : t . . . y = 2x 6, n . . . y=12x+ 32 . 417 .
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n
f
f(x) = x4
f(x) = sin x
f(x) = cos 2x
f(x) = e3x
f(x) = sin2 x
f(x) = ln(1 +x)
f(x) = xex
f(x) = x3 ln x
f(x) = 4x3, f(x) = 12x2, f(x) = 24x, f(4)(x) = 24, f(n)(x) = 0
n 5 f(n)(x) = (1)n2 sin x n f(n)(x) = (1)n12 cos x n
f(n)(x) = (1)n2 2n cos2x n f(n)(x) = (1)n+12 sin2x n
f(n)(x) = (3)ne3x
f(n)(x) = (1)n212n1 cos2x
n
f(n)(x) =
(1)n12 2n1 sin2x n f(n)(x) = (1)n1(n1)!(1+x)n f(n)(x) = (x+n)ex
f(x) = 3x2 ln x+x2, f(x) = 6x ln x+5x, f(x) = 6ln x+11, f(n)(x) = (1)n(n4)!6xn3
n4
f
f(x) = x2x+2
f :0, 4 R f(x) =x(x 3)2
f(x) = x+1
x(x+3)
f(x) = x22x1
x
f(x) = 4x+2
(x1)4
f(x) = x2e
x2
f(x) = ex
1+x
f(x) = x
1+x2
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f(x) = 1x2
4
f(x) = x
x24
f :2, 2 R f(x) =x4 5x2 + 4
f(x) = 11+x2
f(x) = ln
ex
2+ 1
f(x) = 6x3 + 18x2 + 18x+ 6
f(x) = sin(3x+ 1)
R
2R
H
o
P
r
0
0 132 1
+ 2k 3 , k Z
132 + 1
+ 2k 3 k Z R
2
R
H2
2o+4
o+4
R
2 R2
lim
x+(x+ 1)2
x2 + 1
lim
x+1000x
x2 1
lim
x+x2 5x+ 1
3x+ 7
lim
x2x2 3x 4
x4 + 1
limx+
x
x+
x+
x
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1
0
+ 2 1
