Question

$\underset{x\to \infty }{lim}\frac{co{s}^{2}x}{x}=$

• A. 0.0
• B. 1
• C. -1
• D. $\frac{1}{2}$

Answer 1

The correct option is A 0.0

$0\le co{s}^{2}x\le 1$

Dividing throughout inequality by x.

$\frac{0}{x}\le \frac{co{s}^{2}x}{x}\le \frac{1}{x}$ $(x\ne 0)$

Taking $\underset{x\to \infty }{lim}$ throughout the inequality
$\underset{x\to \infty }{lim}0\le \frac{co{s}^{2}x}{x}\le \frac{1}{x}$

$\underset{x\to \infty }{lim}\left(0\right)=0and\underset{x\to \infty }{lim}\frac{1}{x}=0$

Hence, by Sandwich Theorem, $\underset{x\to \infty }{lim}\frac{co{s}^{2}x}{x}=0$