Determine whether the following statements are true and give an explanation or counterexample.

a. Only even powers of x appear in the Taylor polynomials for f(x) = e^-2x centered at 0.

b. Let f(x) = x⁵ - 1. The Taylor polynomial for f of order 10 centered at 0 is f itself.

c. Only even powers of x appear in the nth-order Taylor polynomial for f(x) = √1 + x² centered at 0.

d. Suppose f" is continuous on an interval that contains a, where f has an inflection point at a. Then the second-order Taylor polynomial for f at a is linear.