Find the limit.
-$\lim _ { x \rightarrow 2 } \frac { f ( x ) } { x ^ { 2 } } = 4$, find $\lim _ { x \rightarrow 2 } \frac { f ( x ) } { x }$.
A) 4
B) 16
C) 8
D) 2

Question

Quizplus · Accepted Answer

We can rewrite $\frac{f(x)}{x}$ as $\frac{(x^2)(\frac{f(x)}{x^2})}{x}$, which equals $\frac{x^2(\frac{f(x)}{x^2})}{x}$, or $x(\frac{f(x)}{x^2})$. Taking the limit of this expression as $x$ approaches $2$, we get $2\cdot(\frac{1}{4})$, which equals $\frac{1}{2}$. Therefore, the answer is $\boxed{	extbf{(C)}\ 8}$.

Find the Limit lim⁡x→2f(x)x2=4\lim _ { x \rightarrow 2 } \frac { f ( x ) } { x ^ { 2 } } = 4limx→2​x2f(x)​=4

Find the Limit $\lim _ { x \rightarrow 2 } \frac { f ( x ) } { x ^ { 2 } } = 4$