3+3 roblem 3: [30 pts] Let f(x) = 1 + 4t dt and g(x) = > (x - 1) 2k 2k + 3 k=0 A. [10 pts] Find the Taylor series centered at x = 0 for f(x). In order to receive full credit, you must work entirely in summation notation and write your final answer in summation notation. 3 12 Hint: the sixth degree Taylor polynomial for f(x) centered at x = 0 is x 5 5 + 8x6.B. [6 pts] Calculate g" (1).313 4k Recall that f(x) = dt and g(x) = (x - 1)2k 1 + 4t 2k + 3 k=0 C. [8 pts Find the open interval of convergence for g(x).D. [6 pts] Calculate lim 4f (x) x-0+ 15g(x + 1) - 5 - 12x2 If the limit is infinite, make sure to determine if it is oo or -co. If the limit is finite, simplify your final