If $f$ be a function such that $f(9) = 9$ and $f^{'}(9) = 3$, then $\lim_{x \rightarrow 9}\frac{\sqrt{f(x)} - 3}{\sqrt{x} - 3}$ is equal to

Question

Dr. Abubacker · Accepted Answer

(b)
$\lim_{x ightarrow 9}\frac{\sqrt{f(x)} - 3}{\sqrt{x} - 3} = \lim_{x ightarrow 9}\frac{f(x) - 9}{x - 9} 	imes \frac{\sqrt{x} + 3}{\sqrt{f(x)} + 3}$
$= f^{'}(9) 	imes \left( \frac{\sqrt{9} + 3}{\sqrt{f(9)} + 3} ight)$
$= f^{'}(9) 	imes \frac{3 + 3}{3 + 3} = 3$

Q. If $f$ be a function such that $f(9) = 9$ and $f^{'}(9) = 3$, then $\lim_{x \rightarrow 9}\frac{\sqrt{f(x)} - 3}{\sqrt{x} - 3}$ is equal to

Explanation

Reviewed by Dr. Abubacker

Want more practice?