1. lim tg x
1. lim tg x
1. lim tg x
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1<br />
<strong>1.</strong> <strong>lim</strong><br />
x→0<br />
<strong>tg</strong> x − sin x<br />
x 3<br />
2. <strong>lim</strong><br />
x→0 +<br />
3. <strong>lim</strong><br />
x→∞<br />
ln x<br />
ln (sin x)<br />
π − 2arc<strong>tg</strong> x<br />
ln ( 1 + 1 )<br />
x<br />
4. <strong>lim</strong><br />
x→0<br />
e 2x − 1<br />
arc<strong>tg</strong> 5x<br />
5. <strong>lim</strong><br />
x→0<br />
arcsin 2x − 2 arcsin x<br />
x 3<br />
6. <strong>lim</strong><br />
x→0<br />
3 x − 2 x<br />
x √ 1 − x 2<br />
7. <strong>lim</strong><br />
x→0<br />
e x2 − 1<br />
cos x − 1<br />
8. <strong>lim</strong><br />
x→0<br />
x − arc<strong>tg</strong> x<br />
x 3<br />
9. <strong>lim</strong><br />
x→0<br />
x − <strong>tg</strong> x<br />
x 2 <strong>tg</strong> x<br />
10. <strong>lim</strong><br />
x→1<br />
ln(1 − x)<br />
ln ( sin(1 − x) )<br />
1<strong>1.</strong> <strong>lim</strong><br />
x→0<br />
e x − e −x − 2x<br />
x − sin x<br />
12. <strong>lim</strong><br />
x→1<br />
sin(x − 1) · <strong>tg</strong> πx<br />
2<br />
13. <strong>lim</strong> x 2 · e 1<br />
x 2<br />
x→0<br />
14. <strong>lim</strong> (π − 2arc<strong>tg</strong> x) · ln x<br />
x→∞<br />
15.<br />
(<br />
<strong>lim</strong> x − ln 3 x )<br />
x→+∞<br />
16.<br />
( )<br />
1<br />
<strong>lim</strong><br />
x→0 x − 1<br />
arc<strong>tg</strong> x<br />
17.<br />
( ln(x + 1)<br />
x+1<br />
<strong>lim</strong><br />
x→0 x 2 − 1 )<br />
x<br />
18. <strong>lim</strong><br />
(c<strong>tg</strong> x − 1 )<br />
x→0 x<br />
19.<br />
( (<br />
<strong>lim</strong> x − x 2 ln 1 + 1 ))<br />
x→∞<br />
x<br />
20.<br />
( x<br />
<strong>lim</strong><br />
x→<br />
π<br />
c<strong>tg</strong> x − π )<br />
2 cos x<br />
2<br />
2<strong>1.</strong><br />
( 1<br />
<strong>lim</strong><br />
x→0 x − 1 )<br />
e x − 1
2<br />
22. <strong>lim</strong><br />
( ) cos x π − 2x<br />
x→ π −<br />
2<br />
23. <strong>lim</strong><br />
x→+∞<br />
√<br />
2x π<br />
− arc<strong>tg</strong> 2x<br />
2<br />
1<br />
24. <strong>lim</strong> (π − arcc<strong>tg</strong> x) x+1<br />
x→−∞<br />
25. <strong>lim</strong><br />
x→0<br />
(<br />
arcsin x<br />
) sin x<br />
26. <strong>lim</strong><br />
x→0<br />
(e x + x) 1 x<br />
( ) 1<br />
27. <strong>lim</strong> cos(sin x) x 2<br />
x→0<br />
( ) 1<br />
28. <strong>lim</strong> c<strong>tg</strong> x<br />
ln x<br />
x→0 +<br />
( ) 1<br />
2<br />
29. <strong>lim</strong><br />
x→0 + π arccos x x<br />
30. <strong>lim</strong> x 2<br />
x 2 −1<br />
x→1<br />
( ) 3<br />
3<strong>1.</strong> <strong>lim</strong> cos 2x x 2<br />
x→0<br />
( ) 2x−π<br />
32. <strong>lim</strong><br />
x→<br />
π <strong>tg</strong> x<br />
2<br />
33. <strong>lim</strong><br />
x→0 + xsin x<br />
34. <strong>lim</strong> x 1<br />
1−x<br />
x→1<br />
35. <strong>lim</strong><br />
x→0<br />
(<br />
arcsin x<br />
) <strong>tg</strong> x<br />
<strong>tg</strong> (2x)<br />
36. <strong>lim</strong> (<strong>tg</strong> x)<br />
x→<br />
π<br />
4<br />
37. <strong>lim</strong><br />
(ln 1 ) x<br />
x→0 + x<br />
( ) 2 x<br />
38. <strong>lim</strong><br />
x→∞ π arc<strong>tg</strong> x<br />
( ) 1<br />
arc<strong>tg</strong> x x<br />
39. <strong>lim</strong><br />
x→0 x<br />
( )<br />
(1 + x) 1 1<br />
x<br />
x<br />
40. <strong>lim</strong><br />
x→0 e
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