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Find a power series representation for the given function. Kindly provide complete solutions.
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- The function f(x)=3xarctan(6x) is represented as a power series (image) Find the first few coefficients in the power series.Find a power series for the function f (x) = x2/(1 + x3)Let f(x) = 1 + x 1 X Find the power series representation for the function f(x) by completing the following steps: a. First, express the fraction 1¹ as a power series. = X b. Now, express the fraction as a power series. 1-x 1+x x c. The function f(x) 1-x 1-x + 1 is the sum of the two series from parts (a) and (b). Express the function f(x) as a power series. d. What is the interval of convergence and the radius of convergence for this power series?