"
"
"
x+ x+ x
x
9+2x-5 sin nx 1-cos x sin 5x-sin 3x
" "
lim , lim , lim , lim , lim , lim ,
3
x+1 x-2 sin mx x2 x0 x sin x
x" x8 xĄ x0 x0
" "
x2 1
2 3
3
1+ x ln(x+1)
x2+1 x+1- 16
sin x
lim , lim (1 + x2) x , lim , lim , lim ,
x2-2 1+sin x x x-15
x" x0 x0 x0 x15
1
3
ln(3+x)-ln 3 1- x
x3+3x2+2x 1+2x
x
" x
lim , lim , lim , lim , lim ,
3
x2-x+6 1- 1+ x 1-x x Ä„ 2- x- x
x-2 x0 x0 x0
x
4
" " " "
1-cos 7x
lim 1 + x + x2 - 1 - x + x2 , lim 1 + x + x2 - 1 - x + x2 , lim ,
x2
x+" x-" xĄ
"
" " "
3
3
log5(x-4) x2-2 x+1
cos 2x- 1+x sin x
"x
lim , lim x · arcsin x, lim , lim , lim .
x
2
x-5 (x-1)2 x0 ( ) x
x5 x+0 x1 2 x0
x2-25
x = -5

x-5
f(x) =
-10 x = -5
sin 4x
x = 0

x
f(x) =
2 x = 0
x-sin x
-1 < x < 0
x3
f(x) =
1
0 d" x < 1
2
Ä„
- sin x |x| = 1

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

x+x2
f(x) =
|a + 1| x = 0
ln x x e" 1
f(x) =
ax - 3 x < 1
x2 "
"
x = 0

1+x sin x- cos x
f(x) =
a x = 0
"sin 6x
x = 0

x+4-2
f(x) =
a + 3 x = 0