Question

If $f\left(x\right)=\frac{x-a}{\sqrt{x}-\sqrt{a}}$ is continuous at $x=a$ then $f\left(a\right)$ equals

• A. $\sqrt{a}$
• B. $2\sqrt{a}$
• C. $a$
• D. $2a$

Answer 1

The correct option is B $2\sqrt{a}$

Solution -

$f\left(x\right)=\frac{x-a}{\sqrt{x}-\sqrt{a}}$ is continuous at $x=a$

$f^{\prime }\left(x\right)=\frac{1}{\frac{1}{2\sqrt{x}}}=2\sqrt{x}$ (L-Hospital rule)

$f\left(a\right)=f^{\prime }\left(a\right)=2\sqrt{a}$

B is correct