Question

If $f(4)=g(4)=2 ; f^{\prime}(4)=9 ; g^{\prime}(4)=6$ then $\underset{x \rightarrow 4} {\text{Limit}} \frac{\sqrt{f(x)}-\sqrt{g(x)}}{\sqrt{x}-2}$ is equal to -

• A. $3 \sqrt{2}$
• B. $\frac{3}{\sqrt{2}}$
• C. 0
• D. none of these

Answer 1

Answer: (A)

$\displaystyle\lim _{x \rightarrow 4} \frac{\sqrt{f(x)}-\sqrt{g(x)}}{\sqrt{x}-2}=\displaystyle\lim _{x \rightarrow 4} \frac{\frac{1}{2} \frac{f^{\prime}(x)}{\sqrt{f(x)}}-\frac{1}{2} \frac{g^{\prime}(x)}{\sqrt{g(x)}}}{\frac{1}{2 \sqrt{x}}}$
$=\frac{\frac{9}{\sqrt{2}}-\frac{6}{\sqrt{2}}}{\frac{1}{2}}=3 \sqrt{2}$