Use graphs and tables to find the limit and identify any vertical asymptotes.
-$$\lim _ { x \rightarrow 5 } \frac { 1 } { x ^ { 2 } - 25 }$$
A) $1 ; x = - 5$
B) The limit does not exist; no vertical asymptotes
C) The limit does not exist; $x = - 5$ and $x = 5$
D) 0 ; no vertical asymptotes

Question

Quizplus · Accepted Answer

The given function is $\frac{1}{x^2-25}$, which simplifies to $\frac{1}{(x-5)(x+5)}$. This function is undefined at $x = 5$ and $x = -5$, where the denominator equals zero, leading to vertical asymptotes at these points. As $x$ approaches 5, the function's value approaches infinity or negative infinity, depending on the direction of approach, indicating that the limit does not exist.

Use Graphs and Tables to Find the Limit and Identify lim⁡x→51x2−25\lim _ { x \rightarrow 5 } \frac { 1 } { x ^ { 2 } - 25 }x→5lim​x2−251​

Use Graphs and Tables to Find the Limit and Identify $\lim _ { x \rightarrow 5 } \frac { 1 } { x ^ { 2 } - 25 }$