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STD 11 - 12. limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{{{(1 + x)}^{1/2}} - {{(1 - x)}^{1/2}}}}{x} = $
  • A
    $0$
  • B
    $1/2$
  • ✓
    $1$
  • D
    $-1$
✓

Answer

Correct option: C.
$1$
c
(c) Multiply function by $\frac{{{{(1 + x)}^{1/2}} + {{(1 - x)}^{1/2}}}}{{{{(1 + x)}^{1/2}} + {{(1 - x)}^{1/2}}}}$ and solve.

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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