Multivariable university calculus : early transcendentals by Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.

By Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.

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University Calculus, Early Transcendentals, Multivariable, 3rd Edition is helping scholars generalize and observe the main principles of calculus via transparent and targeted factors, thoughtfully selected examples, meticulously crafted figures, and more suitable workout units. this article bargains the right combination of easy, conceptual, and tough workouts, in addition to significant functions. This revision good points extra examples, extra mid-level workouts, extra figures, better conceptual movement, and the easiest in know-how for studying and teaching.


Note: this article is simply chapters 9-17.


If you will want the entire textual content order ISBN 0321999584  9780321999580  college Calculus, Early Transcendentals, 3/e/Hass / Weir 

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Extra resources for Multivariable university calculus : early transcendentals

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A ln a b n + 1 n=1 e 67. a a p b 86. If gan converges and an 7 0 for all n, can anything be said about gs1>an d ? Give reasons for your answer. 2 + 4 64. a n n n=1 3 + 4 n q 85. Show by example that gsan>bn d may converge to something other than A> B even when A = gan, B = gbn Z 0 , and no bn equals 0. n n=1 q n! 61. a n n = 0 1000 n ƒxƒ 7 1 1 60. a a1 - n b 2n - 1 3n n=0 63. a 84. Find convergent geometric series A = gan and B = gbn that illustrate the fact that gan bn may converge without being equal to AB.

001 1 67. 1 3 n = 2 n sln nd q ln n 64. a n n=2 A q 66. a n=2 q 68. 5 The Ratio and Root Tests 517 70. a. Use Theorem 8 to show that COMPUTER EXPLORATIONS 69. It is not yet known whether the series q q 1 1 1 + a a 2 b S = a nsn + 1d n = 1 nsn + 1d n=1 n q 1 a n 3 sin2 n n=1 q converges or diverges. Use a CAS to explore the behavior of the series by performing the following steps. where S = g n = 1 s1>n 2 d, the sum of a convergent p-series. b. 2, show that q a. Define the sequence of partial sums 1 S = 1 + a 2 .

142857 142857 Á 48. a stan-1 snd - tan-1 sn + 1dd n=1 Convergence or Divergence Which series in Exercises 49–68 converge, and which diverge? Give reasons for your answers. If a series converges, find its sum. q 49. a a n=0 q 1 22 b n q 50. a A 22 B n n=0 q 3 51. a s -1dn + 1 n 2 52. a s -1dn + 1n 53. a cos np 54. a n=1 q n=0 n=1 q n=0 cos np 5n 506 Chapter 9: Infinite Sequences and Series q 1 56. a ln n 3 n=1 2 57. a n n = 1 10 1 58. a n , n=0 x n=0 q q q q n=1 q nn 62. a n = 1 n! q 2 + 3 4n n n 87.

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