Question

If $f\left(1\right)=1,f^{\prime }\left(1\right)=2$, then $\underset{x\to 1}{lim}\frac{\sqrt{f\left(x\right)}-1}{\sqrt{x}-1}$ is

• A. $2$
• B. $4$
• C. $1$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $2$

$\underset{x\to 1}{lim}\frac{\sqrt{f\left(x\right)}-1}{\sqrt{x}-1}=$indeterminate form

Applying L'Hospital rule

$\underset{x\to 1}{lim}\frac{\frac{1}{2\sqrt{f\left(x\right)}}{f}^{\prime }\left(x\right)}{1/2}=2$