Find the limit, if it exists.
-$$\lim _ { x \rightarrow 7 } \frac { | 7 - x | } { 7 - x }$$
A) 0
B) $- 1$
C) Does not exist
D) 1

Question

Quizplus · Accepted Answer

The limit does not exist because the function behaves differently as x approaches 7 from the left and from the right. For $x < 7$, $|7 - x| = 7 - x$, so the fraction simplifies to 1. For $x > 7$, $|7 - x| = -(7 - x) = x - 7$, so the fraction simplifies to -1. Since the left-hand limit and the right-hand limit are different, the overall limit does not exist.

Find the Limit, If It Exists lim⁡x→7∣7−x∣7−x\lim _ { x \rightarrow 7 } \frac { | 7 - x | } { 7 - x }x→7lim​7−x∣7−x∣​

Find the Limit, If It Exists $\lim _ { x \rightarrow 7 } \frac { | 7 - x | } { 7 - x }$