The correct option is B 12aRationalise the given expression. lim_x→ 0√(a+x) √(a)/x×√(a+x)+√(a)/√(a+x)+√(a) =lim_x→ 0a+x a/x(√(a+x)+√(a)) =lim_x→ 01/√(a+x)+√(a) ...

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Byju's Answer

Standard XI

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 0 a+x...

Question

$lim x \to 0 \frac{\sqrt{a + x} - \sqrt{a}}{x} =$
.

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12a

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Solution

The correct option is B 12a
Rationalise the given expression.

$lim x \to 0 \frac{\sqrt{a + x} - \sqrt{a}}{x} \times \frac{\sqrt{a + x} + \sqrt{a}}{\sqrt{a + x} + \sqrt{a}}$

$= lim x \to 0 \frac{a + x - a}{x (\sqrt{a + x} + \sqrt{a})}$

$= lim x \to 0 \frac{1}{\sqrt{a + x} + \sqrt{a}}$

$= \frac{1}{\sqrt{a + 0} + \sqrt{a}}$

$= \frac{1}{2 \sqrt{a}}$

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limx→0 √a+x−√ax = .

The correct option is B 12aRationalise the given expression. limx→0√a+x−√ax×√a+x+√a√a+x+√a =limx→0a+x−ax(√a+x+√a) =limx→01√a+x+√a =1√a+0+√a =12√a

$lim x \to 0 \frac{\sqrt{a + x} - \sqrt{a}}{x} =$
.