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 $\frac{x+3}{(x+3)(x-4)} = \frac{1}{x-4}$ when $x \neq -3$. As $x$ approaches -3, the denominator approaches -7, so the limit 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 }x→−3lim​x2−x−12x+3​

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