Q 5. - Calculus

Question

If $\underset{x\to 2^{+}}{\lim }f\left(x\right)=8$ but $\underset{x\to 2}{\lim }f\left(x\right)$ does not exist, what can you say about $\underset{x\to 2^{-}}{\lim }f\left(x\right)$?

Step-by-Step Solution

Answer

The value of $\underset{x\to 2^{-}}{\lim }f\left(x\right)$ cannot be said as it is unknown.

Step 1. Given information.

It is given that $\underset{x\to 2^{+}}{\lim }f\left(x\right)=8$ and $\underset{x\to 2}{\lim }f\left(x\right)$ does not exist.

Step 2. Determine the value of lim x → 2 - f ( x ) .

The value of $\underset{x\to 2^{+}}{\lim }f\left(x\right)$ is equal to $8$ does not mean that $\underset{x\to 2^{-}}{\lim }f\left(x\right)=8$.

Also, it is given that $\underset{x\to 2}{\lim }f\left(x\right)$ does not exist.

So, the value of $\underset{x\to 2^{-}}{\lim }f\left(x\right)$ cannot be said as it is not given.