If f(@) (0) = (n + 1)! for n = 0, 1, 2, ..., find the Maclaurin series for f. E 7=0 Find its radius of convergence R. R =Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that R, (x) - 0.] f(x) = sin(Itx f(x) = > n = Find the associated radius of convergence R. R =Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R, (x) - 0.] f(x) = x4 - 4x2 + 2, a = 2 O f(2)(x - 2)0 = 2 + 16(x - 2) - 8(x - 2)2 + 20(x - 2)3 - (x - 2)4 n! n = 0 C f(2)(x - 2)0 = -2 + 16(x - 2) + 20(x - 2)2 - 8(x - 2)3 + (x - 2)4 n! n = 0 00 f"(2) (x - 2)0 = -2 - 16(x - 2) + 20(x - 2)~ + 8(x - 2)3 + (x - 2)4 n! n = 0 00 O f (2)( x - 2)0 = 2 + 16(x - 2) + 8(x - 2)2 + 20(x - 2)3 + (x - 2)4 n! n = 0 O f(2)(x - 2)0 = 2 + 16(x - 2) + 20(x - 2)~ + 8(x - 2)3 + (x - 2)4 n! n = 0 X Find the associated radius of convergence R. R =