If $f(1) = 1,\ f^{'}(1) = 2$, then $\lim_{x \rightarrow 1}\frac{\sqrt{f(x)} - 1}{\sqrt{x} - 1}$ is

Question

Dr. Abubacker · Accepted Answer

(a)
$\lim_{x \rightarrow 1}\frac{\sqrt{f(x)} - 1}{\sqrt{x} - 1} = \lim_{x \rightarrow 1}\frac{\sqrt{x} - f'(x)}{\sqrt{f(x)}}$ [by L’ Hospital’s rule]
$= \frac{1.f(1)}{f(1)} = \frac{2}{1} = 2$

Q. If $f(1) = 1,\ f^{'}(1) = 2$, then $\lim_{x \rightarrow 1}\frac{\sqrt{f(x)} - 1}{\sqrt{x} - 1}$ is

Explanation

Reviewed by Dr. Abubacker

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