Practice Midterm 2

Practice Midterm 2 - (1 + x 2 ) 5 . 5. Let f ( x ) = xe x 2...

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Math 127 - Spring 2008 Practice for Second Examination 1. Find the interval of convergence for the power series X n =2 ( - 1) n +1 ( x - 6) 2 n n 12 3 n . 2. Find the MacLaurin series for the function f ( x ) = e x 3 - 1 x 3 . 3. Find the sum of the infinite series 1 2 - 2 2 2 + 3 2 3 - ... + ( - 1) n +1 n 2 n + ... . 4. Find the MacLaurin series for 1
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Unformatted text preview: (1 + x 2 ) 5 . 5. Let f ( x ) = xe x 2 . Estimate R 3 ( x ), the error of the 3rd degee Taylor polynomial approxi-mation centered at 0. 6. Find the Taylor series for f ( x ) = sin( x ) centered at 4 , and nd its radius of convergence. 1...
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