![]() ![]() ) f (x) ln(1x1 x) f (x) n0 ( n) x Graph f and several partial sums sn(x) on the same screen. (Give your power series representation centered at x 0. If I want to find the power series representation of this, the first four. Find a power series representation for f. What is the interval of convergence (c) Use part (b) to nd the sum of the series n1 n 2n. We can represent arctan(2x) with a power series by representing its derivative. What is the interval of convergence (b) Use term-by-term dierentiation to nd a power series representation for the function g(x) 1(1 x)2. ![]() This series converges when ⣠x ⣠< 1 |x| < 1 ⣠x ⣠< 1. (a) Find a power series representation for f(x) 1(1 x). Also, we will be able to find a corresponding change in the domain of the power series representation, since we will be moving the. Example: Can I find a power series representation for the function f (x) 1. My main point is that the power series representation does not exist. Given a function, can I find a power series representation of that function. (Center your power series representation at x 0.) f(x) 1/5 x f(x) sigmainfinityn. ![]() F ( x ) = x 2 tan â¡ â 1 ( x 3 ) f(x) = x^2 \tan^ \\Ä£ x 2 â 1 â ( â x 6 ) 1 â â = 3 x 2 n = 0 â â â ( â x 6 ) n = n = 0 â â â ( â 1 ) n 3 x 6 n 2 = 3 x 2 â 3 x 8 3 x 14 â 3 x 20 . Despite the already fine answers, my take on this subject. Power Series representations of Functions From our knowledge of Geometric Series, we know that g(x) 1 1 x 1 x x2 x3 ::: X1 n0 xnfor jxj<1: IRecall that we had a ar ar2 ar3 X1 n1 arn 1 a 1 r if 1 <1 and this series diverges for jrj 1. Question: Find a power series representation for the function. ![]()
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