Suppose that the power series
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CALCULUS EARLY TRANSCENDENTALS W/ WILE
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- Part IV: Determine whether the following series are convergent or divergent. Use the nth term test for divergence (Corollary 9.9) and the alternating series test. Make sure to check all conditions. sin(k) (i) E (-1)* (E(1/t)) sin(풍서) (iv) E 1 (ii) (iii) k 1+ k cos(k) k k=1 k=1 k=1 k=1 (Hint: Can you say something about sin(k) + sin( (k + 6))?)arrow_forward7. Find a power series representation for the function and determine the interval of convergence. ƒ(x) = X 2x-1arrow_forwardFind the radii of convergence for each of the following power series. (a) (b) (c) n=1 n(x - 1)" 2n (n-1)x", n=1 Hint: The radius of convergence is 1. Explain why you can show this by checking that the series converges for x = -1, but diverges for x = 1. To show the latter, it is helpful to recall that (1+1)* S.M. ≤n. n=2 (x - π)" n(n − 1)*arrow_forward
- 2. I) Find the centre, radius, and interval of convergence for the given power series. 1 -(x+96)³" 3n (13)" n Inn n=2 (II) Determine all values of x where the given power series (a) absolutely convergent and (b) conditionally convergent.arrow_forwardpart D E needarrow_forwardPlease use these questions to find non-zero terms!arrow_forward
- 2n2+5 Does the series E converge or diverge? What happens if I try to use the Ratio Test? Is it better to use the Limit Lun=1 Comparison Test?arrow_forward2. Consider the power series > ak(x + 2)*. Assume that we know that the series ak converges, but that k=0 k=0 ar(4*) diverges. k=0 (a) Does the power series converge at x = -1.3? Explain how you know, or explain why you don't have enough information to answer the question. (b) Does the series > ak (5)* converge or diverge? Explain how you know, or explain why you don't have k=0 enough information to answer the question.arrow_forwarda, b and c please. I'm very confusedarrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning