Lecture 29: 11.10 { Taylor and Maclaurin Series (II)

Lecture 29: 11.10 { Taylor and Maclaurin Series (II) - g x...

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Lecture 29: 11.10 { Taylor and Maclaurin Series (II) ex. Find the Maclaurin series and Taylor Series centered at a = 2 for p ( x ) = x 3 ± 2 x 2 + x ± 3 :
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ex. Find the Maclaurin Series for f ( x ) = e 5 x ex. Find the Maclaurin Series for f ( x ) = xe x
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ex. Find the Taylor Series expansions for f ( x ) = sin x centered at a = ± 4 , then calculate sin 48 ±
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Find the sum of the series: ex. 1 X 0 ( ± 1) n ± 2 n 6 2 n (2 n )! ex. 1 X 0 ( ± 1) n x 4 n n !
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More practice: 1. Find the Taylor Series for f ( x ) = 1 x centered at a = 1. Write your answer in summation notation. What is the radius of convergence? 2. Find the Maclaurin Series for
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Unformatted text preview: g ( x ) = sin( x 2 ) : Use the ±rst 2 non-zero terms of this series to approximate the integral Z 1 sin( x 2 ) dx: 3. Find the Maclaurin series for f ( x ) = x cos x Write your answer in summation notation. 4. Find the MacLaurin series for f ( x ) = ln( x + 1) using the de±nition of a Maclaurin series. Express your answer in summation notation. 5. Find the sum of the series 1 ± ln 2+ ( ln 2) 2 2! ± ( ln 2) 3 3! + ²²²...
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This note was uploaded on 04/19/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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Lecture 29: 11.10 { Taylor and Maclaurin Series (II) - g x...

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