12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-3

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


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