2.1 Q-4

Q4. ${\lim }_{x\to 4}\frac{\sqrt{x}-2}{x-4}$

\section*{Solution:} $\begin{array}{rl}& \underset{x\to 4}{\lim }\frac{\sqrt{x}-2}{x-4}\\ & =\underset{x\to 4}{\lim }\frac{\sqrt{x}-2}{x-4}\times \frac{\sqrt{x}+2}{\sqrt{x}+2}\\ & =\underset{x\to 4}{\lim }\frac{(\sqrt{x}{)}^2-(2{)}^2}{(x-4)(\sqrt{x}+2)}\end{array}$ $={\lim }_{x\to 4}\frac{x<4}{(x-4)(\sqrt{x}+2)}$ $={\lim }_{x\to 4}\frac{1}{\sqrt{x}+2}$ $=\frac{1}{\sqrt{4}+2}$ $=\frac{1}{2+2}$ $=\frac{1}{4}$