Find the indicated limit, if it exists.
- $\lim _ { x \rightarrow 5 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } - 5 - x & x < - 5 \\ 4 & x = - 5 \\ x + 9 & x > - 5 \end{array} \right.$

Question

Find the indicated limit, if it exists.
-$\lim _ { x \rightarrow 5 } f ( x ) , f ( x ) = \left\{ \begin{array} { l l } - 5 - x & x < - 5 \ 4 & x = - 5 \ x + 9 & x > - 5 \end{array} \right.$
A) 0
B) The limit does not exist.
C) 9
D) 4

Quizplus · Accepted Answer

The function is defined piecewise with different expressions for different intervals of $x$. However, the question asks for the limit as $x$ approaches 5, where the function is defined as $x + 9$. This means as $x$ approaches 5, $f(x)$ approaches $5 + 9 = 14$, which is not an option given. The confusion might arise from not carefully reading the intervals for which each piece of the function is defined. Since the correct limit (14) is not listed among the options, the provided options are incorrect based on the question as asked.