Complete the table and use the result to estimate $\lim _{x \rightarrow-2} \frac{x+2}{x^{2}-x-6}$ numerically.

$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & -2.1 & -2.01 & -2.001 & -2 & -1.999 & -1.99 & -1.9 \
\hline f(x) & & & & ? & & & \
\hline
\end{array}$

A) $ -\frac{1}{5} $
B) 5
C) $ \infty $
D) -5
E) limit does not exist

Question

Complete the table and use the result to estimate $\lim _{x \rightarrow-2} \frac{x+2}{x^{2}-x-6}$ numerically.

$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & -2.1 & -2.01 & -2.001 & -2 & -1.999 & -1.99 & -1.9 \
\hline f(x) & & & & ? & & & \
\hline
\end{array}$

A) $ -\frac{1}{5} $
B) 5
C) $ \infty $
D)  -5 
E) limit does not exist

Quizplus · Accepted Answer

The function simplifies to $\frac{1}{x-3}$ when factored and simplified, which is defined at $x = -2$, giving a value of $-\frac{1}{5}$.

Complete the Table and Use the Result to Estimate lim⁡x→−2x+2x2−x−6\lim _{x \rightarrow-2} \frac{x+2}{x^{2}-x-6}limx→−2​x2−x−6x+2​