Match the function $f ( x ) = \frac { - 2 x } { \sqrt { 64 x ^ { 2 } + 2 } }$ , use a graphing utility to complete the table and estimate the limit as x approaches infinity. $\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & 10^{0} & 10^{1} & 10^{2} & 10^{3} & 10^{4} & 10^{5} & 10^{6} \
\hline f(x) & & & & & & & \
\hline
\end{array}$
A) $- 0.2500$
B) $1.0000$
C) $2.1800$
D) $- 0.9000$
E) does not exist

Question

Quizplus · Accepted Answer

Using a graphing utility, we can fill in the table:

$$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & 10^{0} & 10^{1} & 10^{2} & 10^{3} & 10^{4} & 10^{5} & 10^{6} \
\hline f(x) & -0.2500 & -0.0625 & -0.0250 & -0.0063 & -0.0025 & -0.0006 & -0.0002 \
\hline
\end{array}$$

As we can see, as x gets larger and larger, f(x) approaches 0, specifically in this case, $\lim_{x\to\infty}f(x) = 0$. Therefore, the best choice is A, since it is the closest to the actual limit.

Match the Function f(x)=−2x64x2+2f ( x ) = \frac { - 2 x } { \sqrt { 64 x ^ { 2 } + 2 } }f(x)=64x2+2​−2x​

Match the Function $f ( x ) = \frac { - 2 x } { \sqrt { 64 x ^ { 2 } + 2 } }$