A) 1
B) 0
C) \[\sqrt{a}\]
D) \[1/\sqrt{a}\]
Correct Answer: D
Solution :
\[\underset{x\to 0}{\mathop{\text{lim}}}\,\left[ \frac{\sqrt{a+x}-\sqrt{a-x}}{x} \right]\] \[=\underset{x\to 0}{\mathop{\text{lim}}}\,\,\left[ \frac{(\sqrt{a+x}-\sqrt{a-x})(\sqrt{a+x}+\sqrt{a-x})}{x(\sqrt{a+x}+\sqrt{a-x})} \right]\] \[=\underset{x\to 0}{\mathop{\text{lim}}}\,\,\left[ \frac{2x}{x(\sqrt{a+x}+\sqrt{a-x})} \right]=\frac{2}{\sqrt{a}+\sqrt{a}}=\frac{1}{\sqrt{a}}\].
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