1. limit to infinity !!

what is the value of the limit as the function cosx/x tends to infinity??...

2. Originally Posted by anme
what is the value of the limit as the function cosx/x tends to infinity??...
zero.

use the squeeze theorem

3. Originally Posted by anme
what is the value of the limit as the function cosx/x tends to infinity??...
The squeeze theorem is necessary.

Recall that $-1\leqslant\cos x\leqslant 1$.

Modifiying the inequality, we see that $-\frac{1}{x}\leqslant\frac{\cos x}{x}\leqslant\frac{1}{x}$

Taking the limit of each of these terms as x approaches infinity, we see that

$\lim_{x\to\infty}-\frac{1}{x}\leqslant\lim_{x\to\infty}\frac{\cos x}{x}\leqslant\lim_{x\to\infty}\frac{1}{x}\implies 0\leqslant\lim_{x\to\infty}\frac{\cos x}{x}\leqslant0$.

This then suggests that $\color{red}\boxed{\lim_{x\to\infty}\frac{\cos x}{x}=0}$

Does this make sense?

4. Directly put the Limit
Hint:Since cos(x) is somewhere in beteen +/- 1 and x is infinity