Question

True or False: $\underset{x\to c}{\lim }f\left(x\right)$exists and equals some number for any function f as long as c is in the domain of f.

Short answer

The given statement is false.

Step-by-step solution

Step 1. Given information.

Given is the statement

$\underset{x\to c}{\lim }f\left(x\right)$ exists and equals some number for any function fas long as c is in the domain off.

Step 2. Explanation for the given statement to be false.

We need to find whether the given statement is true or false.

The given statement is false since function could be undefined at c, the definition of the limit is the function near c.