"
"
3
3
x2 - 2 x + 1 4x3 - 3x2 + 3
lim , lim ,
x1 x"
(x - 1)2 2x2 + 5x - 1
x2 + x - 6 x2 + x
lim , lim ,
x2 - 2x x3 + 1
x -1
x2
" "
x2 + x - 12
lim , lim x x2 + 3 - x2 - x ,
x3 - 3)2
x"
(x
x2+2x
2x 4x2 + 1
lim , lim ,
x0 x" - 2
3x 4x2
" "
3
4x2 - x + x3 - 2x2 + 2
2
lim x sin 3x x, lim " ,
x0 x"
x + 3x2 + 2x
"
3 - x 2x2 + x3 -x2
lim , lim
x0 x"
x 2x2 + 5
x2 + x - 2 x2 - x - 6
lim , lim ,
x -2
x3 + 4x2 + 4x x -2- x2 + 4x + 4
"
x
lim x 3x, lim ,
x0
x0+ sin 2x - 2x
x3 + 3x2 + x
x
lim , lim arccos ( - 1) ,
x-1+ x2 - 1 x0+
"
9 + 2x - 5 sin nx
lim " , lim ,
3
x8 - 2 sin mx
xĄ
x
ln(3 + x) - ln 3 (x2 + x - 2)
lim , lim ,
x0 x1
x x2 - 1
x2
sin 5x - sin 3x x2 + 1
lim , lim ,
x0 x" - 2
sin x 3x2
" "
1
3
3
sin x
x + 1 - 16 1 + x
lim , lim ,
x15 - 15 1 + sin x
x0
x
2
ln(sin2 x + 1)
x
lim , lim 1 + x2 ,
x0 x0
x2
x3 + 3x2 + 2x x
lim , lim " ,
x-2 - x + 6 1
x0 - 1 + x
x2
1
x
1 + 2x 1 - cos x
lim , lim ,
x0 - x x2
x0
1
3
1 - x log5(x - 4)
lim , lim ,
3
Ä„
x5 - 5
x - x - x x
2
4
x2 + 3x
lim x · arcsin x, lim ,
x+0 x" - 7
2x2
" "
cos 2x - 1 + x sin x x
"
lim , lim ,
2
x0 x0
(x) x
2
10x x3
lim , lim ,
x2 - 2)4 (x + 2)2
x -2
(x
3x 3x - 7
lim , lim ,
x2 - x 4
x2 - 4x + x2
2
sin 5x sin 2x
- sin x
lim , lim arctg
x0 x0
x |x|
tg sin 5x sin(sin 2x)
lim lim
x0 x0
ln(2x + 1) tg(tg3x)
ln(cos 2x) 1 - cos(1 - cos x)
lim lim
x0 x0
ln(cos x) x4
"
1-x-1
32x - 1
lim lim
x0 - 1) 2x
x0
sin(x
Å„Å‚
x2
òÅ‚ - 25 sin 4x
x = -5 x = 0

f(x) = f(x) =
x - 5 x
ół
2 x = 0
-10 x = -5
x - sin x
Ä„
- sin x |x| = 1

-1 < x < 0
2
f(x) = f(x) =
x3
1 x2 - x + 1 |x| > 1
0 d" x < 1
Å„Å‚ 2
ôÅ‚ 5 x < -2
ôÅ‚
ôÅ‚
x
1
ôÅ‚
òÅ‚ + 1 -2 d" x < 0
2
1 3
f(x) =
1 + log1 x + 0 d" x d"
2 2
2
ôÅ‚
ôÅ‚
ôÅ‚ -2
ôÅ‚ 3
ół
x >
2
2x - 3
f(x)
sin 5x
ln x x e" 1
x = 0

f(x) = f(x) =
x + x2
ax - 3 x < 1
|a + 1| x = 0
Å„Å‚ Å„Å‚
x2 sin 6x
òÅ‚ òÅ‚
"
" x = 0 x = 0

"
f(x) = f(x) =
1 + x sin x - cos x x + 4 - 2
ół ół
a + 3 x = 0
a x = 0