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 $x^2 - 169 = (x - 13)(x + 13)$, giving $\frac{x-13}{(x-13)(x+13)}$. As $x$ approaches $13$ from the left, the expression simplifies to $\frac{1}{x+13}$, which equals $\frac{1}{26}$ when $x = 13$.

Find lim⁡x→13−x−13x2−169 \lim _{x \rightarrow 13^{-}} \frac{x-13}{x^{2}-169} limx→13−​x2−169x−13​ A) 126 \frac{1}{26} 261​

Find $\lim _{x \rightarrow 13^{-}} \frac{x-13}{x^{2}-169}$
A) $\frac{1}{26}$