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MATH111-200530-PS10

MATH111-200530-PS10 - MATH111-002 200530 Problem Set 10...

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MATH111-002 200530 Problem Set 10 Edward Doolittle You do not need to hand this one in! You do not need to hand in this problem set! It is provided to help you study for the final exam. 1. (2 marks) Find the radius of convergence and interval of convergence of the following power series. (a) n 0 x n n 1 (b) n 1 x n 3 n ln n 1 (c) n 0 1 n x 2 n n ! (d) n 1 3 x 1 n n 1 2 n 2. (3 marks) Find the Maclaurin series for each of the following functions using the definition of Maclaurin series. (a) f x cos2 x (b) f x e 3 x (c) f x 1 1 x 2 (d) f x e x 1 (e) f x e x e x (f) f x xe x 3. (1 mark) Sum five terms of a Maclaurin series to derive an approximation to e 0 2 . Compare with the value given by your calculator. 4. (1 mark) Use a Maclaurin series derived in the textbook to obtain a Maclaurin series for the given function. (a) f x sin x 2 (b) f x xe x (compare with 2f) 5. (1 mark) Find the Taylor series for f x
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