A) 1
B) zero
C) \[\sqrt{a}\]
D) \[\frac{1}{\sqrt{a}}\]
Correct Answer: D
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{a+x}-\sqrt{a-x}}{x}\times \frac{\sqrt{a+x}+\sqrt{a-x}}{\sqrt{a+x}+\sqrt{a-x}}\] \[\Rightarrow \]\[\underset{x\to 0}{\mathop{\lim }}\,\frac{a+x-(a-x)}{x}\times \frac{1}{\sqrt{a+x}+\sqrt{a-x}}\] \[\Rightarrow \]\[\underset{x\to 0}{\mathop{\lim }}\,\frac{2}{\sqrt{a+x}+\sqrt{a-x}}\Rightarrow \frac{2}{2\sqrt{a}}\Rightarrow \frac{1}{\sqrt{a}}\]
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