Chapter 4.3, Problem 75E

To determine

(a)

To show:

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

To determine

(b)

To show:

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

To determine

(c)

To show:

The inequality $\cos x\le 1-\frac{1}{2}{x}^2+\frac{1}{24}{x}^4$ holds for $x\ge 0$.