Chapter 4.3, Problem 76E

To determine

(a)

To show:

The inequality $e^{-x}\ge 1-x$ holds for $x\ge 0$.

To determine

(b)

To show:

The inequality $e^{-x}\le 1-x+\frac{1}{2}{x}^2$ holds for $x\ge 0$.

To determine

(c)

To show:

The inequality $e^{-x}\ge 1-x+\frac{1}{2}{x}^2-\frac{1}{6}{x}^3$ holds for $x\ge 0$.