3. Given the power series n=0 (a) Simplify an+1 an (-1)(n+1)2(x 2) 9n+2 and find the...

 

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3. Given the power series n=0 (a) Simplify an+1 an (-1)(n+1)2"(x 2)" 9n+2 and find the limit. (b) State the radius of convergence and the endpoints. Substitute to show whether each endpoint is in the interval of convergence or not. (c) It can be shown that the series converges to f(x) = 1 (5+2x) on its interval of convergence. To illustrate this, find $5, $10, and $15. Plot these three polynomials and f on the same set of axes in the window [-4, 9], y [-4, 4]. 3. Given the power series n=0 (a) Simplify an+1 an (-1)(n+1)2"(x 2)" 9n+2 and find the limit. (b) State the radius of convergence and the endpoints. Substitute to show whether each endpoint is in the interval of convergence or not. (c) It can be shown that the series converges to f(x) = 1 (5+2x) on its interval of convergence. To illustrate this, find $5, $10, and $15. Plot these three polynomials and f on the same set of axes in the window [-4, 9], y [-4, 4].