Find $\lim _ { x \rightarrow 9 ^ { - } } \frac { x - 9 } { x ^ { 2 } - 81 }$.
A) $\frac { 1 } { 18 }$
B) $\frac { 1 } { 9 }$
C) $\frac { 9 } { 2 }$
D) $\frac { 2 } { 9 }$
E) limit does not exist

Question

Quizplus · Accepted Answer

The limit can be simplified by factoring the denominator as $(x-9)(x+9)$ and then canceling out the $(x-9)$ term, leaving $\frac{1}{x+9}$. As $x$ approaches $9$ from the left, the expression simplifies to $\frac{1}{18}$.

Find lim⁡x→9−x−9x2−81\lim _ { x \rightarrow 9 ^ { - } } \frac { x - 9 } { x ^ { 2 } - 81 }limx→9−​x2−81x−9​

Find $\lim _ { x \rightarrow 9 ^ { - } } \frac { x - 9 } { x ^ { 2 } - 81 }$