1) 1/2√a
2) 4/4√a
3) 1/3√a
4) 2/√a
Solution: (2) 4/4√a
\(\begin{array}{l}\begin{array}{l} \lim _{x \rightarrow 0}\left(\frac{\sqrt{a+x}-\sqrt{a-x}}{4 x}\right) \\ \text { Apply } L \text { ‘ hospital rule }\left(\frac{0}{0} \text { form }\right) \\ \lim _{x \rightarrow 0} \frac{\frac{1}{2 \sqrt{a+x}}-\frac{1 \times-1}{2 \sqrt{a-x}}}{4 \times 1} \\ \Rightarrow \frac{\frac{1}{2 \sqrt{a+0}}+\frac{1}{2 \sqrt{a-x}}}{4} \Rightarrow \frac{\frac{1}{2 \sqrt{a}}+\frac{1}{2 \sqrt{a}}}{4}\\ \Rightarrow \frac{4}{4 \sqrt{a}} \end{array}\end{array} \)
