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Unformatted text preview: = ∞ s n =0 x n (1) Find the MacLaurin series of the function g ( x ) = 1 (1x ) 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 ( x4) 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 satis±es 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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 Spring '10
 DONALDSON,NEIL
 Calculus, Maclaurin Series, Taylor Series

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