Chapter9B

# Chapter9B - Chapter 9 Practice Test B 1 Tell whether the...

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Unformatted text preview: Chapter 9 Practice Test B 1. Tell whether the series n 1 5 3 4 n converges or diverges. If it converges, find its sum. 2. Find the Taylor polynomial of order 3 generated by f x x cos 3 x at 3. . 3 Let f be a function that has derivatives of all orders for all real numbers. Assume f 0 9, f 0 5, f 0 4, and f 0 36. Write the third order Taylor polynomial for f at x 0 and use it to approximate f 0.3 . The Maclaurin series for f x 2x a b c 3 x2 4 x3 5 x4 6 … 2 Find f 0 . Let g x xf x 4. is n n 1 1 xn …. x . Write the Maclaurin series for g x . Let h x 0 f t dt. Write the Maclaurin series for h x . 1 1 x2 5. Find the Taylor polynomial of order 4 for f x and use it to approximate f 0.2 . at x 0 6. 7. The polynomial 1 on the interval 6x 0.02 15 x2 is used to approximate f x 1 x6 x 0.02. Find the maximum absolute error. Determine the convergence or divergence of each series. Identify the test or tests you use. a n 1 n3 2n 1 b n 1 1 1 5n 2n c n 1 1 n2 n 8. Determine whether each series converges absolutely, converges conditionally, or diverges. a n 1 1 n n 1 1 3 3 b n 1 1 3n n 1 n4 c n 1 cos n 4 n n3 9. Find the radius of convergence of each power series. a n 0 4x 7n n b n 1 3x n 4 5n n 10. Find the interval of convergence of the series n 0 4x 9n 5 2n and, within this interval, the sum of the series as a function of x. 11. Determine all values of x for which the series n 1 n 2n cosn x converges. 12. Find the interval of convergence of the series n 0 2 n x 2 1 3n n . n 13. Given that sin x n 0 1 2n n x2 n 1 1 , provide a power series x 2 3 representation for 14. Find 15. Find 16. Find Pn x Pn x Pn x and and and fx Rn x Rn x Rn x x sin for for for fx fx fx x4, c sin x, c 16, and 4 n 3 5 n 2 , and n 0, and 3 1 x2 , c ...
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