Chapter 11, Problem 83CR

To determine

To evaluate: the limit if exists and verify it graphically.

Answer to Problem 83CR

Yes, the limit exists and it is $3$ .

Explanation of Solution

Given:

  $\underset{x\to \infty }{\lim }\left(3-\frac{1}{x^2}\right)$

Solving the given limit,

  $\underset{x\to \infty }{\lim }\left(3-\frac{1}{x^2}\right)=3$

Yes, the limit exists and it is 3.

Now, verifying graphically,

  

It can be seen that at infinity, the limit of function is $3$ .