A) 1
B) 0
C) -1
D) 2
Correct Answer: C
Solution :
Let\[L=\underset{x\to 0}{\mathop{\lim }}\,\,\frac{f({{x}^{2}})-f(x)}{f(x)-f(0)}\] |
Using L.H. Rule, we get \[L=\underset{x\to 0}{\mathop{\lim }}\,\,\frac{f'({{x}^{2}}).2x-f'(x)}{f'(x)}\] |
\[=\underset{x\to 0}{\mathop{\lim }}\,\,\frac{f'({{x}^{2}}).2x}{f'(x)}-1\] \[\left[ \begin{align} & \because \,\,f'\,(a)>0,f\,\,being \\ & strictly\,\,\text{increasing} \\ \end{align} \right]\] |
\[=0-1=-1\] |
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