(c) (2 points) Using your function f(x) from (b), find the exact answer to 2n + 2 n! n=0 by evaluating C f(x)dx, where c is the bound you found in part (a).Consider the infinite series i 1 .i nz02n+2 n!- In this problem, we are going to use Taylor series to find the exact value. (a) (4 points) Due to the factors of the form 1/(2n + 2) in the sum, we might suspect that this is actually the integral of some power series. That is, 0 1 1 0 exp" g2n+2im2 nldx' where c > 0 is a fixed number and pn is some sequence of numbers. Find suitable values of c and 1),, so that the above is an equality. (b) (4 points) In (a), you obtained a power series 00 xpn Z n; n=0 This is, in fact, the Taylor series of some function f(x) centred at x = 0. Using the Taylor series of familiar functions like polynomials, the exponential, logarithms, etc., find this function f(x)