Chapter 2, Problem 1PE

To determine

To state the informal definition of a limit of a function.

Explanation of Solution

Calculation:

Let the function $f\left(x\right)$ .

The limit of a function $f\left(x\right)$ is $L$ and $L\in R$ , as x approaches c, and $c\in R$ .

such that

  $\underset{x\to c}{\lim }f\left(x\right)=L$

If the value of function $f\left(x\right)$ can be made arbitrarily close to limit $L$ by selecting the value of x closest to c.

This informal definition help to find the limit of a function at point c, if the limitexists.

But it will never make sure completely if the limit of function exists.

This is because x not approaches point c as we want.