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Unformatted text preview: = s n =0 x n (1) Find the MacLaurin series of the function g ( x ) = 1 (1-x ) 2 (2) What are the radius of convergence of the MacLaurin series of the function f ( x ) and g ( x )? Problem 5 (15 points) Find the interval of the convergence J for the power series s n =1 1 n 5 n ( x-4) n and check whether this series converges or diverges at two end points of J . Problem 6 (15 points) Suppose that f ( x ) is a function which satises the equation f ( x ) =-f ( x ) for all x and f (0) = 1 (1) Determine the MacLaurin series of f ( x ). (2) What is the expression of f ( x ). 2...
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This note was uploaded on 03/11/2012 for the course MATH 2J 44360 taught by Professor Donaldson,neil during the Spring '10 term at UC Irvine.
- Spring '10