Limx- a-3x-a - -x-a-x-a -

Lim_x→ a(√(3x a)) (√(x+a))/x a = lim_x→ ∞(√(3x a)) (√(x+a))/x a × (√(3x a)) + (√(x+a))/(√(3x a))+(√(x+a))) = 2/2(√(2a)) = 1/(√(2a)) Aliter: Apply L Hospita ...

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Byju's Answer

Standard XIII

Mathematics

Rationalization Method to Remove Indeterminate Form

limx→ a√3x-a ...

Question

$l i m_{x \to a}$ $\frac{(\sqrt{3 x - a}) - (\sqrt{x + a})}{x - a}$ =

$\sqrt{2 a}$

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

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$\frac{1}{2 a}$

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Solution

The correct option is B $\frac{1}{\sqrt{2 a}}$
$l i m_{x \to a}$ $\frac{(\sqrt{3 x - a}) - (\sqrt{x + a})}{x - a}$ = $l i m_{x \to \infty}$ $\frac{(\sqrt{3 x - a}) - (\sqrt{x + a})}{x - a}$ × $\frac{(\sqrt{3 x - a}) + (\sqrt{x + a})}{(\sqrt{3 x - a}) + (\sqrt{x + a}))}$ = $\frac{2}{2 (\sqrt{2 a})}$ = $\frac{1}{(\sqrt{2 a})}$
Aliter:- Apply L-Hospital's rule

$l i m_{x \to a}$ $\frac{(\sqrt{3 x - a}) - (\sqrt{x + a})}{x - a}$ = $l i m_{x \to \infty}$ $\frac{3}{2 (\sqrt{3 x - a})}$ - $\frac{1}{2 (\sqrt{x + a})}$ = $\frac{3}{2 (\sqrt{2 a})}$ - $\frac{1}{(2 \sqrt{2 a})}$ = $\frac{1}{(\sqrt{2 a})}$

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limx→a(√3x−a)−(√x+a)x−a =

$l i m_{x \to a}$ $\frac{(\sqrt{3 x - a}) - (\sqrt{x + a})}{x - a}$ =