MCQ
$\mathop {\lim }\limits_{x \to 0} \,\left[ {\frac{{\sqrt {a + x} - \sqrt {a - x} }}{x}} \right] = . . .$
- A$1$
- B$0$
- C$\sqrt a $
- ✓$1/\sqrt a $
$ = \mathop {{\rm{lim}}}\limits_{x \to 0} \,\left[ {\frac{{(\sqrt {a + x} - \sqrt {a - x} )(\sqrt {a + x} + \sqrt {a - x} )}}{{x(\sqrt {a + x} + \sqrt {a - x} )}}} \right]$
$ = \mathop {{\rm{lim}}}\limits_{x \to 0} \,\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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