Find the indicated limit, if it exists.
- $\lim _ { x \rightarrow 0 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } 8 - x ^ { 2 } & x < 0 \\ 8 & x = 0 \\ 2 x + 8 & x > 0 \end{array} \right.$

Question

Find the indicated limit, if it exists.
-$\lim _ { x \rightarrow 0 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } 8 - x ^ { 2 } & x < 0 \ 8 & x = 0 \ 2 x + 8 & x > 0 \end{array} \right.$
A) The limit does not exist.
B) 8
C) 2
D) $- 6$

Quizplus · Accepted Answer

The limit as $x$ approaches 0 from the left is $8 - 0^2 = 8$, and the limit as $x$ approaches 0 from the right is $2(0) + 8 = 8$. Since both one-sided limits are equal to 8, the limit of $f(x)$ as $x$ approaches 0 exists and is equal to 8.

Find the Indicated Limit, If It Exists A) the Limit Does Not Exist