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workshop11

# workshop11 - opitals Rule if you used it(Dont try it Look...

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Workshop 11 1) a) Use the formula a 1 - r = a + ar + ar 2 + ar 3 + · · · valid for | r | < 1 to express each of the following functions as a power series a 0 + a 1 x + a 2 x 2 + · · · + a n x n + · · · . Give a formula for the coefficient a n in each case. f ( x ) = x 1 - x ; g ( x ) = 2 3 x 4 + 16 , b) Determine the interval of x values in which each series in part a) converges (be sure to consider the endpoints). c) Use your answer to a) to express 1 0 2 3 x 4 + 16 dx as the sum of an infinite series. 2) Compute lim x 0 (sin 3 x - 3 x ) 2 ( e 2 x - 1 - 2 x ) 3 . Use Maclaurin series (Taylor series centered at 0) that you know, instead of L’Hˆ opital’s Rule. How many times would you have had to apply L’Hˆ
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Unformatted text preview: opitals Rule if you used it? (Dont try it! Look at the Maclaurin series to tell.) 3) In the following series x is a real number. In each case use the ratio test to determine the radius of convergence of the series. Analyze the behavior of the series at the endpoints in order to determine the interval of convergence. a) X n =0 nx n n 2 + 1 b) X n =1 n 2 ( x-1) n 2 n c) X n =1 3 n x n n 2 1...
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