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Download Calculo Diferencial e Integral – Tomo I by N. Piskunov PDF

By N. Piskunov

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Extra resources for Calculo Diferencial e Integral – Tomo I

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A sln nd2 n3 n 3 q 26. a n=1 q 29. a 2n 3 + 2 1 1 31. a n = 1 1 + ln n 2n ln n ln sn + 1d 32. a n + 1 n=2 2n 34. a 2 n=1 n + 1 1 - n 35. a n n = 1 n2 n=1 q q n=2 q q 51. 3 1 n n2n q 49. a n=1 q coth n n2 n 2n 52. a 2 n=1 n 1 54. a 2 2 2 n=1 1 + 2 + 3 + Á + n n: q 60. Suppose that an 7 0 and lim n 2an = 0. Prove that gan conn: q verges. q sin2 n n n=1 2 19. a q 22. a n + 1 n 2 2n q 3 5n - 3n 24. a 2 n sn - 2dsn 2 + 5d n=3 1 n=1 q 59. Suppose that an 7 0 and lim an = q . Prove that gan diverges. Determining Convergence or Divergence Which of the series in Exercises 17–54 converge, and which diverge?

Use the accompanying graph to show that the partial sum s50 = g n = 1 A 1> 2n + 1 B satisfies 50 n 1 28. a a1 + n b n=1 q 44. Are there any values of x for which g n = 1s1>nxd converges? Give reasons for your answer. ˆ 2 25. a n=1 n + 1 q T b. There is absolutely no empirical evidence for the divergence of the harmonic series even though we know it diverges. The partial sums just grow too slowly. To see what we mean, suppose you had started with s1 = 1 the day the universe was formed, 13 billion years ago, and added a new term every second.

An = n tan-1 n 1 2 + ƒsxn d . ƒ¿sxn d Do the sequences converge? If so, to what value? In each case, begin by identifying the function ƒ that generates the sequence. n 1 x dx -1 , b. The fractions rn = xn>yn approach a limit as n increases. What is that limit? ) 87. an = n - 2n 2 - n 2n 2 - 1 - 2n 2 + n 1 89. an = n or 103. Pythagorean triples A triple of positive integers a, b, and c is called a Pythagorean triple if a 2 + b 2 = c 2 . Let a be an odd positive integer and let b = j a2 k 2 and c = l a2 m 2 be, respectively, the integer floor and ceiling for a 2>2 .

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