Determine $\lim _ { x \rightarrow 10 } \frac { | x - 10 | } { x ^ { 2 } - 100 }$ (if it exists)by evaluating the corresponding one-sided limits.
A) $\frac { 1 } { 20 }$
B) $- \frac { 1 } { 20 }$
C)0
D)10
E)limit does not exist

Question

Quizplus · Accepted Answer

The limit does not exist because the one-sided limits as $ x \to 10^+ $ and $ x \to 10^- $ are not equal. The expression simplifies to $\frac{1}{20}$ for $ x > 10 $ and $-\frac{1}{20}$ for $ x < 10 $.

Determine lim⁡x→10∣x−10∣x2−100\lim _ { x \rightarrow 10 } \frac { | x - 10 | } { x ^ { 2 } - 100 }limx→10​x2−100∣x−10∣​

Determine $\lim _ { x \rightarrow 10 } \frac { | x - 10 | } { x ^ { 2 } - 100 }$