Chapter 12.2, Problem 54E

To determine

To find: whether the statement is true or false.

Answer to Problem 54E

The above statement is false.

Explanation of Solution

Given information:

Given statement

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

Calculation:

To check the correctness of the statement, compare it with definition of limit of the function.

Limit of the function is defined if and only if the value 0 the function at a given point is same as the variable approaches the point both left and right. And also the value of the function is same at the point.

As the statement does not provide information about the one sided limit of the function at the defined, hence the statement is false.