Chapter 12.1, Problem 69E

To determine

To write: a brief description of the meaning of the notation $\underset{x\to 5}{\lim }f\left(x\right)=12$ .

Answer to Problem 69E

The value of the function is 12 as $x$ is equal to 5.

Explanation of Solution

Definition of limit of the function Limit of the function $f\left(x\right)$ is $f\left(c\right)$ if and only if as $x$ approaches $c$ from both left and right of $c$ is $f\left(c\right)$ and also the value of the function is $f\left(c\right)$ , when $x=c$ .

Thus the statement $\underset{x\to 5}{\lim }f\left(x\right)=12$ signifies the following.

Limit of the function $f\left(x\right)$ is 12 as $x$ approaches 5 from both left and right of 5 and also the value of the function is 12 as $x$ is equal to 5.