116pexam02 - 4. Use power series to evaluate Z e (5 x-3000)...

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Practice Exam #2 1. Determine convergence or divergence for the following series. Be sure to state your reasoning. (a) X n =2 1 n ln n (b) X n =1 ( - 1) n 5 n 4 n +1 (c) X n =1 2 n 4 - n 2 (d) X n =1 1 2 n + 3 (e) X n =1 3 n 4 n 2 + 7 n + 17 2. Find the interval of convergence for X n =0 n 3 ( x - 5) n . 3. Find the Taylor Series of f ( x ) = x 1 / 2 at x = 4. Provide at least ±ve terms.
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Unformatted text preview: 4. Use power series to evaluate Z e (5 x-3000) 2 + 2 dx. 5. Use power series to solve the dierential equation y-x 2 y = 0 . If you choose not to nd a pattern, provide at least ve nonzero terms....
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