Let $f ( x ) = \left\{ \begin{array} { c l } 2 x ^ { 2 } & x < - 2 \\4 & x = - 2 \\x + 10 & x > - 2\end{array} \right.$ Which of the following is true for $\lim _ { x \rightarrow - 2 } f ( x )$ ?

Question

Let $f ( x ) = \left\{ \begin{array} { c l } 
2 x ^ { 2 } & x < - 2 \
4 & x = - 2 \
x + 10 & x > - 2
\end{array} \right.$ Which of the following is true for $\lim _ { x \rightarrow - 2 } f ( x )$ ?

A)4
B)6
C)8
D)10
E)Does not exist

Quizplus · Accepted Answer

The left-hand limit as $x$ approaches $-2$ is $2(-2)^2 = 8$ and the right-hand limit is $-2 + 10 = 8$. Since both limits are equal, $\lim _ { x \rightarrow - 2 } f ( x ) = 8$.

Let f(x)={2x2x<−24x=−2x+10x>−2f ( x ) = \left\{ \begin{array} { c l } 2 x ^ { 2 } & x < - 2 \\4 & x = - 2 \\x + 10 & x > - 2\end{array} \right.f(x)=⎩⎨⎧​2x24x+10​x<−2x=−2x>−2​

Let $f ( x ) = \left\{ \begin{array} { c l } 2 x ^ { 2 } & x < - 2 \\4 & x = - 2 \\x + 10 & x > - 2\end{array} \right.$