Find $\lim _ { x \rightarrow 13 ^ { - } } \frac { x - 13 } { x ^ { 2 } - 169 }$.
A) $\frac { 1 } { 26 }$
B) $\frac { 1 } { 13 }$
C) $\frac { 13 } { 2 }$
D) $\frac { 2 } { 13 }$
E) limit does not exist

Question

Quizplus · Accepted Answer

The limit can be simplified by factoring the denominator as $(x-13)(x+13)$ and then cancelling the $(x-13)$ term, leaving $\frac{1}{x+13}$. As $x$ approaches $13$ from the left, the expression simplifies to $\frac{1}{26}$.

Find lim⁡x→13−x−13x2−169\lim _ { x \rightarrow 13 ^ { - } } \frac { x - 13 } { x ^ { 2 } - 169 }limx→13−​x2−169x−13​

Find $\lim _ { x \rightarrow 13 ^ { - } } \frac { x - 13 } { x ^ { 2 } - 169 }$