Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.a. The Taylor polynomials for f(x) = e?2x consist of even powers only.b. For f(x) = x5 ? 1, the Taylor polynomial of order 10 centered at x = 0 is f itself.c. The nth-order Taylor polynomial for centered at 0 consists of even powers of x only.

Solution 65EStep 1:In this problem we have to check whether the given statements are true or not.a. The Taylor polynomials for consist of even powers only.The given statement is false.Reason: Let us find the taylor polynomial for The Taylor series is given by For n=0 For n=1 For n=2 For n=3 ….Thus the taylor polynomial is Therefore Hence the Taylor polynomials for consists of both even and odd powers.So the given statement is wrong.