Chapter 12.1, Problem 65E

To determine

To find: whether the statement is true or false.

Answer to Problem 65E

The statement is true.

Explanation of Solution

Given information:

Given statement

The limit of a function as $x$ approaches $c$ does not exist when the function approaches -3 from the left of $c$ and 3 from the right of $c$ .

Calculation:

When a function, $f\left(x\right)$ satisfies any of the following conditions, then the limit of the function does not exist

First $f\left(x\right)$ approaches a different number from the right side of $c$ than it approaches from the left side $f\left(c\right)$ .

Second $f\left(x\right)$ increases or decreases without bound as $x$ approaches $c$ .

Third $f\left(x\right)$ oscillates between two fixed values as $x$ approaches $c$ .

As the function approaches two different numbers from the right side of $c$ than it approaches from the left side $f\left(c\right)$ , the limit at the point does not exist.

Hence the above statement is true $f\left(x\right)$ .