Find $\lim _ { x \rightarrow 5 } [ g ( x ) - f ( x ) ]$ for $f ( x ) = 4 x ^ { 3 }$ and $g ( x ) = \frac { \sqrt { x ^ { 2 } + 5 } } { 3 x ^ { 2 } }$ .
A) $\frac { 20 \sqrt { 30 } } { 3 }$
B) limit does not exist
C) $\frac { \sqrt { 6 } } { 3 } + 500$
D) $\frac { \sqrt { 6 } } { 3 } - 500$
E) $\frac { \sqrt { 30 } } { 75 } - 500$

Question

Quizplus · Accepted Answer

To find the limit, evaluate $g(x)$ and $f(x)$ as $x$ approaches 5. $f(x) = 4x^3$ becomes 500. For $g(x)$, substitute $x = 5$ to get $\frac{\sqrt{30}}{75}$. The limit is $\frac{\sqrt{30}}{75} - 500$.

Find lim⁡x→5[g(x)−f(x)]\lim _ { x \rightarrow 5 } [ g ( x ) - f ( x ) ]limx→5​[g(x)−f(x)]

Find $\lim _ { x \rightarrow 5 } [ g ( x ) - f ( x ) ]$