Calcolare i seguenti limiti, motivando le risposte. log( n14 ) n→+∞ n2 n 5 2. lim 1− n→+∞ n 1. 3. 2n4 + e−n n→+∞ 5 log n + n3 4. (−1)n 2 + 5n + n→+∞ n 7 + 3n 5. 6. [0] lim [e−5 ] lim [+∞] [ 35 ] lim 1 (3 + sin(2n))n p n lim 2n5 + 1 [0] lim n→+∞ [1] n→+∞ n20 + 4n4 + 1 n→+∞ n! √ n 8. lim 2n + 3 n 7. lim [0] [3] n→+∞ 9. 10. n2n n→+∞ 3n lim lim n→+∞ [0] n! − (n + 1)! n2 en 11. n! + 2n n→+∞ (n + 1)! 12. lim 3n+1 − 3 [0] lim √ 13. 14. [−∞] n2 −1 [−∞] n→+∞ n + sin n − n2 + 1 p lim n n log n lim [0] n→+∞ n3 [1] n→+∞ 15. n2 (log n)2 √ n→+∞ n5 + 1 [0] 16. n2 + n sin n n→+∞ 1 + n2 + n [1] lim lim 3n − (−2)n n→+∞ 3n+1 + (−2)n+1 " 4 # 2 18. lim n 1 − 1 − n→+∞ n 17. [ 31 ] lim [8] 1 n! 1 n→+∞ nn nn 1 20. lim 1+ n→+∞ n! n n+1 21. lim n→+∞ n − 1 19. lim [0] 1+ [+∞] [e2 ] 1 − (−1)n √ n→+∞ n r n n 3 23. lim n→+∞ n √ 5 n + n4 − 1 √ 24. lim n→+∞ 4n2 + 1 22. 25. 26. 27. lim [0] [3] [ 12 ] lim n2−n [0] n→+∞ 1 lim n2 2 n [+∞] n→+∞ 2 lim n n [1] n→+∞ 28. arctan n n→+∞ n + (−1)n [0] 29. en n→+∞ nn + 2 [0] 30. √ log3 n + 3 n n→+∞ n − n2 [0] 31. lim lim lim lim n→+∞ log(n + 1) log(n − 1) [1] log(n3 − 1) n→+∞ log(3n4 − 6) p p 33. lim n2 + n − n2 + 1 32. lim [ 43 ] n→+∞ [ 12 ] √ 3 n 34. lim 2 n→+∞ 2n 35. 2 [0] √ lim 2n − 3 n [+∞] n→+∞ 2
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