Question

find the limit.

$\underset{x\to \infty }{\lim }\cos x$

Short answer

The value of limit of the given function $\text{does not exist}.$

Step-by-step solution

Step 1. Given information.

The limit of function is given here,

$\underset{x\to \infty }{\lim }\cos x$

Step 2. Formula used.

Here, in the given question we know the value of $\cos x$ is between $-1$ and $1$ .

Step 3. Simplification.

Given, $\underset{x\to \infty }{\lim }\cos x$

$=\cos \infty$

As we know the value of cos lies between $-1$ to $1$ .

There is no exact values defined for them. $\infty$is undefined thus, $\cos \infty$ cannot have exact defined values.

Therefore, our final answer is limit does not exist.