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

A)-1
B)1
C)2
D)-2
E)Does not exist

Question

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

A)-1
B)1
C)2
D)-2
E)Does not exist

Quizplus · Accepted Answer

The limit as $x$ approaches 2 from the left is $1 - 2 = -1$, and from the right is $1 + 2 = 3$. Since these two one-sided limits are not equal, the overall limit does not exist.

Let f(x)={1−xx≤21+xx>2f ( x ) = \left\{ \begin{array} { l l } 1 - x & x \leq 2 \\1 + x & x > 2\end{array} \right.f(x)={1−x1+x​x≤2x>2​

Let $f ( x ) = \left\{ \begin{array} { l l } 1 - x & x \leq 2 \\1 + x & x > 2\end{array} \right.$