The function f(x) = 3x arctan(8x) is represented as a power series 00 f(x) = Σ cnx". n=0 Find the first few coefficients in the power series. Co = C1 = C₂ = C3 = C4 = Find the radius of convergence R of the series. R = Hint: Notice that d dx - -arctan(8x) = 8 1+64x²' , SO 1 ³/₁ 8 1 + 64x² Can you find a power series representation for a power series representation of 3x arctan(8x)? dx = arctan(8x) + C. 8 -? Integrating that (and finding the value of C) will give you a power series representation for arctan(8x). How do you then adjust to get 1 + 64x²

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