Determine $\lim _ { x \rightarrow 6 } \frac { | x - 6 | } { x ^ { 2 } - 36 }$ (if it exists)by evaluating the corresponding one-sided limits.
A)6
B)0
C)limit does not exist
D) $- \frac { 1 } { 12 }$
E) $\frac { 1 } { 12 }$

Question

Quizplus · Accepted Answer

The limit does not exist because the one-sided limits as $ x \to 6^+ $ and $ x \to 6^- $ are not equal. The expression simplifies to different values on either side of 6 due to the absolute value in the numerator.

Determine lim⁡x→6∣x−6∣x2−36\lim _ { x \rightarrow 6 } \frac { | x - 6 | } { x ^ { 2 } - 36 }limx→6​x2−36∣x−6∣​

Determine $\lim _ { x \rightarrow 6 } \frac { | x - 6 | } { x ^ { 2 } - 36 }$