Consider this function defined by an integral: f(x) = f* arctan(3t) t 0 (a) Find the power series representation centered at x = 0. Complete the given equation. Answer: f(x) = Σ 71=0 dt. (b) Enter the first 5 nonzero terms of the power series.

Use a power series to represent the function f(x) : = Provide your answer below: ΣΠ n = 0 14 9x 2 I centered at X = = -3.

Exercise 3. (i) Show that g(x) = cos(kx) 3k k=1 defines a continuous function g : [0, ] → R. (ii) Compute 플 6.³ g(x) dx. You can leave your answer in the form of a power series.

Use the substitution method to find the power series representation of the function using the formula 00 Σ 1 1-x n=0 f (x) = 1+2x