Complete the table and use the result to estimate $\lim _{x \rightarrow-3} \frac{x+3}{x^{2}-x-12}$ numerically.
$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & -3.1 & -3.01 & -3.001 & -3 & -2.999 & -2.99 & -2.9 \
\hline f(x) & & & & ? & & & \
\hline
\end{array}$
A) $ -\frac{1}{7} $
B) 7
C) $ \infty $
D) $ -7 $
E) limit does not exist

Question

Complete the table and use the result to estimate    $\lim _{x \rightarrow-3} \frac{x+3}{x^{2}-x-12}$  numerically.
$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & -3.1 & -3.01 & -3.001 & -3 & -2.999 & -2.99 & -2.9 \
\hline f(x) & & & & ? & & & \
\hline
\end{array}$
A) $ -\frac{1}{7} $
B) 7
C) $ \infty $
D) $ -7 $
E) limit does not exist

Quizplus · Accepted Answer

The function simplifies to $\frac{1}{x-4}$ after factoring and canceling out $x+3$, so the limit as $x$ approaches -3 is $-\frac{1}{7}$.

Complete the Table and Use the Result to Estimate lim⁡x→−3x+3x2−x−12\lim _{x \rightarrow-3} \frac{x+3}{x^{2}-x-12}limx→−3​x2−x−12x+3​

Complete the Table and Use the Result to Estimate $\lim _{x \rightarrow-3} \frac{x+3}{x^{2}-x-12}$