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 limit of the function as $x$ approaches $-2$ can be found by substituting values of $x$ close to $-2$ into the function and observing the trend. The function simplifies to $\frac{1}{x+3}$ after factoring the denominator as $(x+2)(x-3)$ and canceling out the $x+2$ term. Substituting values close to $-2$ from both sides will show that the function approaches $-\frac{1}{5}$, as the denominator approaches $1$.

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 }x→−2lim​x2−x−6x+2​

Complete the Table and Use the Result to Estimate $\lim _ { x \rightarrow - 2 } \frac { x + 2 } { x ^ { 2 } - x - 6 }$