Find a power series representation for the function. (Center your power series representation at x = 0.) f(x) = 1 / (9 + x) f(x) = sum_{n = 0}^infinity ( ) Determine the interval of convergence. (Enter your answer using interval notation.) DETAILS SCALC8 11.9.008. Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x / (3x^2 + 1) f(x) = sum_{n = 0}^infinity ( ) Determine the interval of convergence. (Enter your answer using interval notation.)
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This is a simple function, and its power series representation is just itself, i.e., f(x) = 9 + x. The interval of convergence for this power series is all real numbers, or (-∞, ∞), because it's a polynomial and polynomials are defined for all real numbers. Show more…
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