Utilizzando i limiti notevoli determinare, se esistono, i seguenti limiti

Utilizzando i limiti notevoli determinare, se esistono, i seguenti limiti di funzioni:
1 − cos 4x
x→0
8x2
sen5x
x→0 2x
1. lim
2. lim
3x − 1
x→0
2x
7. lim
tg2 x
11. lim 2
x→0 x
log(1 + ex )
10. lim
x→+∞ (1 + ex )5
√
√
1/ x
x→0
lim
3
√
x
x
x→+∞
19. lim 4log x log3 x
x→0
1 − cos x
22. lim
x→0 sen2 x
5senx − 1
x→0
tghx
26. lim
30.
34. lim
x→0
lim
x→+∞
q
23.
27. lim
x→+∞
x→0
(1 + arcsenx)1/arcsenx
39.
√
x)6 − 1
√
lim x2 ex
x→−∞
9.
lim
16. lim
x→0
√
x
√
lim (senhx)2 5senhx
−1
x
(1 + arctgx)5 − 1
x→0
arctg5x
17. lim
x→0
coshx
21. lim
24. lim (1 + senx)2/senx
x→0
28.
2senhx
x→+∞ senhx
log2 (1 + 3x)
√
x
x→−∞
20. lim (arcsenx)4 log(arcsenx)
1
coshx
x→0
x3
4
13. lim
1+ 3
x→−∞
x
1 − cos 5x
12. lim
x→0
senx
2
5. lim
x→0
arctg(senhx)
senhx
log(1 + senx)
x→0
tgx
25. lim
(−coshx)3
x→−∞
4coshx
x1/4
s
senhx
√
2
senhx
1 − cos x
2
31. lim
32.
lim
33.
lim
1
+
x→+∞
x→0 4x2
x→0
senx
senhx
√
log(1 + x)
ex − 1
(1 + senhx)3 − 1
√
√
35. lim
36. lim
37. lim
x→0
x→0 1 − cos x
x→0
6x
senx
(1 +
log(1 + log x)
(1 + log x)3
√
log x
38. lim √
x→+∞
2 log x
lim
1+
x→0
3coshx
x→+∞ (coshx)5
8.
log(1 + 3x)
15. lim
x→0
tghx
14. lim (1 + 7 x)
4. lim (1 + x)1/2x
lim
(1 + 4x)5 − 1
x→0
4x
6. lim
18.
3x
2
1+
x→+∞
x
3.
lim
29.
40. lim (senhx)3 log(senhx)
x→0
lim
Risposte:
1.
5
2
14. e7
15. 3
26. log 5
38. 0
3. e6
2. 1
16. log 2
27. 0
39. 0
4.
28. +∞
40. 0
√
e
5. 0
17. 1
29. 0
6.
log 3
2
18. +∞
30. 0
7. 5
19. 0
31.
1
4
8. +∞
20. 0
32.
1
2
9. 0
10. 0
21. 1
22.
33. e
34.
1
2
√
e
11. 1
12. 0
13. e4
23. e
24. e2
25. 1
35. 1
36. 2
37.
1
2

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