SalasSV_10_04_ex - 10.4 SOME IMPORTANT LIMITS 609 It...

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Unformatted text preview: 10.4 SOME IMPORTANT LIMITS 609 It follows that ln 1 + x n n x and therefore 1 + x n n = e ln(1 + x / n ) n e x . EXERCISES 10.4 State whether the sequence converges as n ; if it does, find the limit. 1. 2 2 / n . 2. e / n . 3. 2 n n . 4. log 10 n n . 5. ln ( n + 1) n . 6. 3 n 4 n . 7. x 100 n n ! . 8. n 1 / ( n + 2) . 9. n / n , > 0. 10. ln n + 1 n . 11. 3 n + 1 4 n 1 . 12. n e 2 x dx . 13. ( n + 2) 1 / n . 14. 1 1 n n . 15. n e x dx . 16. 2 3 n 1 7 n + 2 . 17. n n dx 1 + x 2 . 18. n e nx dx . 19. ( n + 2) 1 / ( n + 2) . 20. n 2 sin n . 21. ln n 2 n . 22. 1 + 1 / n 1 + 1 / n dx 1 x 2 . 23. n 2 sin n . 24. n ! 2 n . 25. 5 n + 1 4 2 n 1 . 26. 1 + x n 3 n . 27. n + 1 n + 2 n . 28. 1 1 / n dx x . 29. n + 1 n e x 2 dx . 30. 1 + 1 n 2 n . 31. n n 2 n 2 . 32. 1 / n cos e x dx . 33. 1 + x 2 n 2 n . 34. 1 + 1 n n 2 . 35. 1 / n 1 / n sin x 2 dx . 36. t + x n n , t > 0, x > 0. c In Exercises 37 and 38, use technology (graphing utility or CAS) to determine whether the sequence converges, and if it does, give the limit.the limit....
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This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.

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SalasSV_10_04_ex - 10.4 SOME IMPORTANT LIMITS 609 It...

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