Chapter 11.1, Problem 65E

a.

To determine

Whether the statement “Only even powers of x appear in the Taylor polynomials for $f\left(x\right)=e^{-2x}$ centered at 0” is true or false.

b.

To determine

Whether the statement “Let $f\left(x\right)=x^5-1$ the Taylor polynomial for f of order 10 centered at 0 is f itself” is true or false.

c.

To determine

Whether the statement “Only even powers of x appear in the nth-order Taylor polynomial for $f\left(x\right)=\sqrt{1+x^2}$ centered at 0” is true or false.

d.

To determine

Whether the statement “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” is true or false.