For the function $f ( x ) = \frac { - x } { \sqrt { 4 x ^ { 2 } - 8 } }$ , use a graphing utility to complete the table and estimate the limit as x approaches infinity. $\begin{array}{lllllll}
x & 10^{0} & 10^{1} & 10^{2} & 10^{3} & 10^{4} & 10^{5}\
f(x)
\end{array}$
A)-1.15
B)0.75
C)-0.5
D)1.93
E)does not exist

Question

Quizplus · Accepted Answer

As $x$ approaches infinity, the function $f(x) = \frac{-x}{\sqrt{4x^2-8}}$ simplifies to $\frac{-x}{\sqrt{4x^2}}$ because the $-8$ becomes negligible. This simplifies further to $\frac{-x}{2x} = -\frac{1}{2}$, indicating that the limit as $x$ approaches infinity is $-0.5$.

For the Function f(x)=−x4x2−8f ( x ) = \frac { - x } { \sqrt { 4 x ^ { 2 } - 8 } }f(x)=4x2−8​−x​

For the Function $f ( x ) = \frac { - x } { \sqrt { 4 x ^ { 2 } - 8 } }$