question_answer

, then \[\underset{x\to 0}{\mathop{lim}}\,\left[ \frac{f'x}{x} \right]\]is:

A) 0                     

B) 2              

C) \[-2\]                            

D) 6

Correct Answer: D

Solution :

[d] \[\Rightarrow -sinx\left( 0-2 \right)-1\left( 0-4x \right)=2sinx+4x\] \[\Rightarrow \underset{x\to 0}{\mathop{lt}}\,\frac{f'(x)}{x}=\underset{x\to 0}{\mathop{lt}}\,\left( \frac{2\sin x}{x}+4 \right)=2\left( \underset{x\to 0}{\mathop{lt}}\,\frac{\sin x}{x} \right)+4\]\[=2\times 1+4=6\]