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Unformatted text preview: Name: Section: MAC 2312 Homework 4 Due April 3, 2012 SHOW ALL OF YOUR WORK L2526: Representing Functions as Power Series 1. Find a power series representation for the function f ( x ) = x 4 + 9 x 2 . Include the interval of convergence. 1 2. Find a power series representation for the function f ( x ) = x 3 (1 x ) 2 . Include the interval of convergence. 2 3. Find a power series representation for the function f ( x ) = arctan(2 x ) . Include the interval of convergence. 3 4. Find a power series representation for the function f ( x ) = ln(5 x ) . Include the interval of convergence. 4 5. Find a power series representation for a function F satisfying both F ′ ( x ) = 1 1 + x 5 and F (0) = √ 2 . 5 L2728: Taylor and Maclaurin Series 6. Find the Taylor series for f ( x ) = 1 x centered at a = 1. Include the radius of convergence. 6 7. (a) Find the Maclaurin series for f ( x ) = sin( x 2 )....
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This note was uploaded on 03/27/2012 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.
 Spring '08
 Bonner
 Calculus, Power Series

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