Find $\lim _ { x \rightarrow 15 ^ { - } } \frac { x - 15 } { x ^ { 2 } - 225 }$.
A) $\frac { 1 } { 30 }$
B) $\frac { 1 } { 15 }$
C) $\frac { 15 } { 2 }$
D) $\frac { 2 } { 15 }$
E) limit does not exist

Question

Quizplus · Accepted Answer

The limit can be simplified by factoring the denominator as $(x-15)(x+15)$ and then canceling out the $(x-15)$ term in the numerator and denominator, leaving $\frac{1}{x+15}$. As $x$ approaches $15$ from the left, the expression simplifies to $\frac{1}{30}$.

Find lim⁡x→15−x−15x2−225\lim _ { x \rightarrow 15 ^ { - } } \frac { x - 15 } { x ^ { 2 } - 225 }limx→15−​x2−225x−15​

Find $\lim _ { x \rightarrow 15 ^ { - } } \frac { x - 15 } { x ^ { 2 } - 225 }$