Question

$\underset{x\to a}{lim}f\left(x\right)$ exists if and only if

1. $\underset{x\to a}{lim}+f\left(x\right)and\underset{x\to a}{lim}-f\left(x\right)$ exist finitely

2. $\underset{x\to a}{lim}+f\left(x\right)=\underset{x\to a}{lim}-f\left(x\right)=f\left(a\right)$

• A. True
• B. False

Answer 1

The correct option is B

False

For $\underset{x\to a}{lim}f\left(x\right)$ to exist, we want right hand limit and left hand limit to exist finitely and equal. While

finding limit, we are not concerned about f(a).So the second statement is not correct. Limit can exist

even if is not equal to the value of the function at the point