Complete the table and use the result to estimate
$$\lim _ { x \rightarrow - 8 } \frac { x + 8 } { x ^ { 2 } + 4 x - 32 }$$
numerically.
$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & -8.1 & -8.01 & -8.001 & -8 & -7.999 & -7.99 & -7.9 \
\hline f(x) & & & & ? & & & \
\hline
\end{array}$

A) $- \frac { 1 } { 12 }$
B) 12
C) $\infty$
D) $- 12$
E) limit does not exist

Question

Complete the table and use the result to estimate
$$\lim _ { x \rightarrow - 8 } \frac { x + 8 } { x ^ { 2 } + 4 x - 32 }$$
numerically.
$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & -8.1 & -8.01 & -8.001 & -8 & -7.999 & -7.99 & -7.9 \
\hline f(x) & & & & ? & & & \
\hline
\end{array}$

A) $- \frac { 1 } { 12 }$
B) 12
C) $\infty$
D) $- 12$
E) limit does not exist

Quizplus · Accepted Answer

The limit of the function as $x$ approaches $-8$ can be estimated by evaluating the function at values close to $-8$ from both sides. The function simplifies to $\frac{1}{x+4}$ after factoring and canceling out $(x+8)$ from the numerator and denominator. Thus, as $x$ approaches $-8$, the function approaches $-\frac{1}{12}$.

Complete the Table and Use the Result to Estimate lim⁡x→−8x+8x2+4x−32\lim _ { x \rightarrow - 8 } \frac { x + 8 } { x ^ { 2 } + 4 x - 32 }x→−8lim​x2+4x−32x+8​

Complete the Table and Use the Result to Estimate $\lim _ { x \rightarrow - 8 } \frac { x + 8 } { x ^ { 2 } + 4 x - 32 }$