Question

If (x) is differentiable and strictly increasing function, then the value of $\lim_{h \rightarrow 0}\frac{f\left( x^{2} \right) - f(x)}{f(x) - f(0)}$ is

• A. 1
• B. 0
• C. −1
• D. 2

Answer 1

Answer: (C)

−1

Answer 2

$\lim_{x \rightarrow 0}\frac{f\left( x^{2} \right) - f(x)}{f(x) - f(0)}$

Using L.H. Rule

$\lim_{x \rightarrow 0}\frac{f'\left( x^{2} \right).2x - f'(x)}{f'(x)} = \lim_{x \rightarrow 0}\frac{f'\left( x^{2} \right).2x}{f'(x)} - 1 = 0 - 1 = - 1$