A) 0
B) 1
C) 2
D) \[-1\]
E) \[-2\]
Correct Answer: B
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{x}{\sqrt{1+x}-\sqrt{1-x}}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{x}{\sqrt{1+x}-\sqrt{1-x}}\times \frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{x(\sqrt{1+x}+\sqrt{1-x})}{1+x-1+x}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{x(\sqrt{1+x}+\sqrt{1-x})}{2x}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\] \[=\frac{2}{2}=1\]You need to login to perform this action.
You will be redirected in
3 sec