Q 6. - Calculus

Question

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

Step-by-Step Solution

Answer

The solution is $\underset{x\to -1}{\lim }f\left(x\right)=-\infty$.

Step 1. Given information.

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

Step 2. Determine the value of lim x → - 1 f ( x ) .

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

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