1-Limits(1)[1]

2x 1

ln(3 2 x)

ln(2 x)

31. lim

.

x 1

x

ln x 1

sin

x

2e

1. lim

.

x e

x e

ln tgx

1/( x / 4)

3. lim

.

x / 4

1 ctgx

4. lim(sin x)3 /(1 x) .

x 2

sin 3 x sin2 ( x 2)

5. lim

.

x 2 sin x

6. lim (sin x)6 x / .

x / 6

7. lim(2

x

)sin x .

x 3

3

1 x (1 x2

_/(1 x)

8. lim

.

x 1 2

x

9. lim(1 ex )

sin x

1 x .

x 1

tg9x x /( x 1)

10. lim

.

x 1

sin 4x

arcsin( x 3) x2 8

11. lim

.

sin 3 x

x 3

x2 2 /16

12. lim (sin 2x)

x / 4 .

x

/ 4

x 3/ 4

x 1

13. lim arctg

.

2

(x 1)

x 1

14. lim(ctg

x

)

sin(x )

.

4

x

sin x sin a x2 / a2

15. lim

.

x a

x a

1/ x

x 2 2

16. lim

.

x2 4

x 2

17.

lim (sin x cos x)1/ tgx.

x / 4

18.

lim (tg 2x)sin( / 8 x) .

x / 8

19.

lim(arcsin x)tg x .

x 1

20.

lim(x sin x)sin x x .

x

21.

lim(ln

2

1/( x2

1)

.

ex)

x 1

22.

lim(

x 1) / arctgx.

x 1

x

3 1 1/ x2

23.

lim

.

x 1 x 1

esin x

1

x2 1

24.

lim

.

x 1

x 1

25.

lim(cos x)tg ( x 2) .

x 2

1

26.

lim (arcsin x arccos x) x .

x 1/ 2

27.

lim (cos x 1)sin x .

x / 2

28.

lim(3

x x 1)sin( x / 4) .

x 1

x

2

2x 3

1/(2 x)

29.

lim

.

2

4x

5

x 1 x

1 cos x

x2

30.

lim

.

2

x 1

tg x

31.

lim((e2 x e2 ) /( x 1))x 1.

x 1

4. lim

tg cos(1/ x) lg( 2 x)

.

x 0

lg( 4 x)

e1/ n sin

n

cos n

n2

1

5.

lim

.

1 cos(1/ n)

n

4

2 n5 2n3 3

6.

lim

.

(n sin n)

n

7n

x

3

tgx (4x ) cos

7.

lim

4x

.

x / 4

lg( 2 tgx)

n

8.

lim(sin

n2 1arctg

).

n

n2 1

9.

lim

n2

3n5 7

.

2 n cos n

n (n

1)

n

10.

lim

3sin n

n

1

.

n

n

n 1

(1 cos n)3

11.

lim

n

.

2n 1 1

n

12.

lim ln(2

arctgx sin

1

).

x 0

x

13.

lim

1 cos x

.

x

x 2

4 (x 2)sin

x 2

14.

lim

n

.

4

n 3

n

3

sin n

15.

lim

3

n2 cos n

3n

2 2

.

5

6

1

n

n