MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{{{(1 + x)}^{1/2}} - {{(1 - x)}^{1/2}}}}{x} = $
- A$0$
- B$1/2$
- ✓$1$
- D$-1$
Aliter : Apply $ L-$ Hospital’s rule,
$\mathop {\lim }\limits_{x \to 0} \,\frac{{{{(1 + x)}^{1/2}} - {{(1 - x)}^{1/2}}}}{x} = \mathop {\lim }\limits_{x \to 0} \,\frac{1}{{2\sqrt {1 + x} }} + \frac{1}{{2\sqrt {1 - x} }} = 1$.
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