Q 3. - Calculus

Question

If $\underset{x\to 1^{-}}{\lim }f\left(x\right)=5$ and $\underset{x\to 1^{+}}{\lim }f\left(x\right)=5$, what can you say about $\underset{x\to 1}{\lim }f\left(x\right)$? What can you say about $f\left(1\right)$?

Step-by-Step Solution

Answer

The value of $\underset{x\to 1}{\lim }f\left(x\right)=5$ and $f\left(1\right)=5$.

Step 1. Given information.

It is given that $\underset{x\to 1^{-}}{\lim }f\left(x\right)=5$ and $\underset{x\to 1^{+}}{\lim }f\left(x\right)=5$.

Step 2. Find lim x → 1 f ( x ) and f ( 1 ) .

Since the left side limit $\underset{x\to 1^{-}}{\lim }f\left(x\right)$ and the right side limit $\underset{x\to 1^{+}}{\lim }f\left(x\right)$ both have same value.

Hence, $\underset{x\to 1}{\lim }f\left(x\right)=5$ and $f\left(1\right)=5$.