Find the limit.
-If $\lim _ { x \rightarrow 0 } \frac { f ( x ) } { x ^ { 2 } } = 4$, find $\lim _ { x \rightarrow 0 } \frac { f ( x ) } { x }$.
A) 2
B) 8
C) 16
D) 4

Question

Quizplus · Accepted Answer

We can rearrange the first limit equation to get $f(x)=4x^2+o(x^2)$ as $x$ approaches 0. Then, we can plug this into the second limit to get $\lim_{x\rightarrow 0}\frac{f(x)}{x} = \lim_{x\rightarrow 0}\frac{4x^2+o(x^2)}{x}=4\cdot\lim_{x\rightarrow 0}(4x)=\boxed{8}$ by using basic limit rules.

Find the Limit lim⁡x→0f(x)x2=4\lim _ { x \rightarrow 0 } \frac { f ( x ) } { x ^ { 2 } } = 4limx→0​x2f(x)​=4

Find the Limit $\lim _ { x \rightarrow 0 } \frac { f ( x ) } { x ^ { 2 } } = 4$