Chapter 9.4, Problem 7QR

To determine

Tostate: that the inequality is correct or not.

Answer to Problem 7QR

Theinequality is correct.

Explanation of Solution

Given information:

Theinequality is $\left|\frac{\cos x}{x^2}\right|\le \frac{1}{x^2},-\infty <x<\infty$ .

to state the inequality, first solve the inequality,

  $\begin{array}{l}\left|\frac{\cos x}{x^2}\right|\le \frac{1}{x^2}\\ \cos x\le 1\text{ [divide out }{x}^2]\end{array}$

The inequality is correct because for all value of x , $-1\le \cos x\le 1$ .