Calculus 2-A7 - Calculus II Calculus: Early Transcendental...

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Calculus II Calculus: Early Transcendental Functions , 4th ed., by Ron Larson, Robert Hostetler, and Bruce H. Edwards (Boston: Houghton Mifflin, 2007; ISBN-10: 0-618-60624-6). Written Assignment 7 Complete the following textbook exercises for sections 9.5 and 9.6, and submit them to your mentor for correction and grading. Show all calculations. SECTION 9.5 Exercises Do exercises 14, 18, 24, 50, and 56 on page 637 of the textbook. In Exercises 11– 32, determine the convergence or divergence of the series. a n =1/(ln(n+1)) lim n -> ∞ a n = lim n ->∞ 1//(ln(n+1)) =0 n+1<n+2 for all n>0 ln(n+1) < ln(n+2) 1/(ln(n+1)) > 1/(ln(n+2)) Therefore a n + 1 < a n for all n>0 Alternating series test are satisfied and therefore the series converges a n = n 2 /(n 2 +5) =>alternating series lim n -> ∞ a n = lim n ->∞ n 2 /(n 2 +5) = lim n ->∞ 1/(1+5/n 2 ) = 1 Since the limit ≠ 0, the series diverges by the nth term test. = ∑ n =1
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Calculus 2-A7 - Calculus II Calculus: Early Transcendental...

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