Question

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

• A. 1
• B. 0
• C. –1
• D. 2

Answer 1

Answer: (C)

–1

Answer 2

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

Apply L' Hospital rule

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

f '(x) is strictly increasing function so that f '(x) > 0

Ž $\frac{f'(0)(2 \times 0) - f'(0)}{f'(0)}$

Ž – $\frac{f'(0)}{f'(0)}$ = – 1