Use graphs and tables to find the limit and identify any vertical asymptotes.
-$$\lim _ { x \rightarrow 7 } \frac { 1 } { ( x - 7 ) ^ { 2 } }$$
A) $- \infty ; x = - 7$
B) $\infty ; x = - 7$
C) 1 ; no vertical asymptotes
D) $\infty ; x = 7$

Question

Quizplus · Accepted Answer

The limit as $x$ approaches 7 of $\frac{1}{(x-7)^2}$ goes to infinity because the denominator approaches 0, making the fraction infinitely large. There is a vertical asymptote at $x = 7$ because the function is undefined at $x = 7$ and approaches infinity as $x$ gets closer to 7 from both sides.

Use Graphs and Tables to Find the Limit and Identify lim⁡x→71(x−7)2\lim _ { x \rightarrow 7 } \frac { 1 } { ( x - 7 ) ^ { 2 } }x→7lim​(x−7)21​

Use Graphs and Tables to Find the Limit and Identify $\lim _ { x \rightarrow 7 } \frac { 1 } { ( x - 7 ) ^ { 2 } }$