Determine $\lim _ { x \rightarrow 1 } f ( x )$ where $f ( x ) = \left\{ \begin{array} { l }
15 - x ^ { 2 } , x \leq 1 \
12 - x , x 1
\end{array} \right.$ (if it exists)by evaluating the corresponding one-sided limits.
A)limit does not exist
B)11
C)12
D)14
E)15

Question

Determine $\lim _ { x \rightarrow 1 } f ( x )$ where $f ( x ) = \left\{ \begin{array} { l } 
15 - x ^ { 2 } , x \leq 1 \
12 - x , x > 1
\end{array} \right.$ (if it exists)by evaluating the corresponding one-sided limits.
A)limit does not exist
B)11
C)12
D)14
E)15

Quizplus · Accepted Answer

The limit as $x$ approaches 1 from the left is $f(x) = 15 - x^2 = 15 - 1^2 = 14$. The limit as $x$ approaches 1 from the right is $f(x) = 12 - x = 12 - 1 = 11$. Since these two one-sided limits are not equal, the overall limit does not exist.

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