138assgn9 - MATH 138 Assignment 9 Spring 2009 Power series...

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Unformatted text preview: MATH 138 Assignment 9 Spring 2009 Power series (part II). Taylor series Submit all problems marked (*) by 4:30 p.m. on Monday , July 20. 1. Find the power series representation for the function and determine the interval of convergence. (a) ( * ) f ( x ) = 3 1- x 4 . (b) ( * ) f ( x ) = 1 x +10 . (c) f ( x ) = x 2 x 2 +1 . (d) f ( x ) = 1+ x 1- x . (e) ( * ) f ( x ) = x 2 a 3- x 3 . (f) f ( x ) = x 2 (1- 2 x ) 2 . (g) ( * ) f ( x ) = arctan( x/ 3). 2. Express the function as the sum of a power series by first using partial fractions. Find the interval of convergence. (a) f ( x ) = 3 x 2- x- 2 . (b) ( * ) f ( x ) = x +2 2 x 2- x- 1 . 3. (a) Find a power series representation for f ( x ) = ln(1+ x ). What is the radius of convergence? (b) ( * ) Use 3a to find a power series for f ( x ) = x ln(1+ x ). What is the radius of convergence? (c) ( * ) Use 3a to find a power series for f ( x ) = ln( x 2 + 1). What is the radius of convergence?...
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138assgn9 - MATH 138 Assignment 9 Spring 2009 Power series...

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