Use graphs and tables to find the limit and identify any vertical asymptotes.
-$$\lim _ { x \rightarrow 5 ^ { - } } \frac { 1 } { x - 5 }$$
A) $- \infty ; x = - 5$
B) $- \infty ; x = 5$
C) $\infty ; x = - 5$
D) 1 ; no vertical asymptotes

Question

Quizplus · Accepted Answer

As $x$ approaches 5 from the left ($x \rightarrow 5^-$), the denominator of the fraction $\frac{1}{x-5}$ approaches 0, causing the value of the fraction to decrease without bound (become more negative), which means the limit is $-\infty$. The expression has a vertical asymptote at $x = 5$, where the denominator equals zero and the function is undefined.

Use Graphs and Tables to Find the Limit and Identify lim⁡x→5−1x−5\lim _ { x \rightarrow 5 ^ { - } } \frac { 1 } { x - 5 }x→5−lim​x−51​

Use Graphs and Tables to Find the Limit and Identify $\lim _ { x \rightarrow 5 ^ { - } } \frac { 1 } { x - 5 }$