Find a power series representation for the function. (Center your power series representation at x = 0.) f(x) = 1 / (3 + x) f(x) = sum from n=0 to infinity of ( ) Determine the interval of convergence. (Enter your answer using interval notation.) Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x^2 / (x^4 + 81) f(x) = sum from n=0 to infinity of ( ) Determine the interval of convergence. (Enter your answer using interval notation.)
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Since this is a simple polynomial, the power series representation is just the polynomial itself. So, we have: f(x) = 3 + x Now, we need to determine the interval of convergence. Since this is a polynomial, it converges for all x. Show more…
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