"
x + 6 - 2
lim
x-2
x3 + 8
2
x
x2 + 1
lim
x" - 2
x2
2x+2 - 16
lim
x2 - 24
4x
sin(x - 1)
lim "
x1
2 - 5 - x2
1 1
e3
48 2

x - 1
lim ex ·
x1
|x - 1|
1
4-x2
lim e( )
x2
8
lim
x
x0 - 2
1

1
lim
x1
1 - x
Ä„ Ä„
e -e " -
2 2
Å„Å‚ "
1 + x
ôÅ‚ - 1
ôÅ‚
òÅ‚ " , x = 0

x
f(x) =
ôÅ‚
ôÅ‚
ół
0 , x = 0
Å„Å‚
ôÅ‚cos Ä„x |x| d" 1
,
òÅ‚
2
f(x) =
ôÅ‚
ół|x - 1|, |x| > 1
x = -1

Å„Å‚
ôÅ‚ + cos x - 1 x = 0
,
òÅ‚
x · |x|
f(x) =
ôÅ‚
ół
0 , x = 0
Å„Å‚
ôÅ‚  , x = 0
ôÅ‚
òÅ‚
f(x) =
sin 5x
ôÅ‚
ôÅ‚
" , x = 0

ół
x + 4 - 2
 = 20
1
y =
x
y = 3x2 - x + 4
1
y = 2x +
x
"
3
y = x

2
y = ln(2x + 4x2 + 1) y = "
4x2 + 1
y = cos4 3x y = -12 sin(3x) · cos3(3x)
-1
y = arcsin(1 - 2x) y =
x(1 - x)
2 -1
y = " y = "
x x · (x + 4)
2 2
y = x2x y = 2x2x +1 · (2 ln x + 1)
2 ln x
y = (sin x) 2x y = (sin x) 2x( + 2x · x)
2x cos2
"
1"
y = xx y = xx · (ln x + 1)
2
1
x
e
f(x) =
x
1
f (-1) - 1
e
1
f ( ) - 4(2e2 + 1)
2
2
f (-1) - 1
e
1
f ( ) 16(5e2 + 1)
2
y = ex · sin x + sin 2x
y - 2y + 2y = -2 sin 2x - 4 cos 2x
f(x) = x3 · (x + 4)
(-", -3) (-3, ")
y = 2x3 + 3x2 - 12x + 1 ymax = y(-2) = 21
" "
x3 3
y = ymax = y( 3) = - 3
x2 - 1 2
" "
3
3
y = (x2 - 4)2 ymin = y( 3) = 3
2
"
3
y = x · e-x ymax = y(0) = 2 2
2x 1
y = ymin = y(2) =
x2 + 4 2
1 1
y = x · ln x ymin = y( ) = -
r e
ex - e-x + 3x
lim 5
x0
x
ln sin x
lim 1
ln sin 2x
x0+

1 1 1
lim -
x0
x ex - 1 2

lim (x - 1) · ln(x - 1) 0
x1+
lim (x - 1)x-1 1
x1+
x-2
1
lim ln 0
x - 2
x2+
2x
1
lim x
Ä„
x e
4
2y = x2 2y = 8 - x2
4
3
"
x3
y = x " ( 3, +")
x2 + 1
y = x - 2ex x "
y = 3x - 6x + 1 x "
y = arccos x x " (-1, 0)
x4 - 3
y = (-1, 2), (1, -2)
x
y = x3 - 3x2 + 3x + 1 (1, 2)
2
y = x · e-x (2, )
e2
y = ln2 x (e, 1)
x
y =
x2 - x - 12
x = 3, x = 4, y = 0

y = 9 - x2
x = -3 x = 3 y = 0
y = ln(1 - x)
x = 1
ln x
y = 2x + 3 +
x
x = 0 y = 2x + 3
"f(x) df(x)
2x - 1
f(x) = , x0 = 0, "x = 1 "x = 0.3
3x + 2
f(x) = ln cos x, n = 3
1
f(x) = , n = 4
1 + x
1 - x
f(x) = , x " 0, 1
1 + x
"
f(x) = xe- x, x " 1, 16