Lim x - a-3 x-a-x-a-x-a-

The correct option is A lim_x→ a nbsp;(√(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)) = ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → a√3 x...

Question

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B

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

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

Suggest Corrections

Similar questions

{lim}_{x \to a} \frac{\sqrt{a + 2 x} - \sqrt{3 x}}{\sqrt{3 a + x} - 2 \sqrt{x}}

Q. Solve :

lim x \to a \frac{\sqrt{a + 2 x} - \sqrt{3 x}}{\sqrt{3 a + x} - 2 \sqrt{x}}

Evaluate

lim x \to a \frac{\sqrt{a + 2 x} - \sqrt{3 x}}{\sqrt{3 a + x} - 2 \sqrt{x}}, a \neq 0

lim x \to a \frac{\sqrt{a + 2 x} - \sqrt{3 x}}{\sqrt{3 a + x} - 2 \sqrt{x}} (a \neq 0)

Evaluate

\begin{matrix} l i m x \to a \end{matrix} \frac{\sqrt{a + 2 x} - \sqrt{3 x}}{\sqrt{3 a + x} - 2 \sqrt{x}} (f r o m \frac{0}{0})

Join BYJU'S Learning Program

limx→a(√3x−a)−(√x+a)x−a =

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