limx→3⁡(√3x-3)/(√(2x-4)- √2) is equal to

Correct answer: (A) 1/(√2). Given, limx→3⁡(√3x-3)/(√(2x-4)- √2) On rationalization we get, limx→3⁡(3x-9×√(2x-4)+ √2)/(2x-4-2×√3x+3) = limx→3⁡(3x-3)/(2x-3)×(√(2x-4)+ √2)/(√3x+3) =3/2×(2√2)/6=1/(√2).

Q60 / 90 · JEE Main 2017 (08 Apr Online) · Mathematics

$\lim_{x \to 3} \frac{\sqrt{3 x} - 3}{\sqrt{2 x - 4} - \sqrt{2}}$ is equal to

Correct answer
A
$\frac{1}{\sqrt{2}}$
B
$\frac{1}{2 \sqrt{2}}$
C
$\frac{\sqrt{3}}{2}$
D
$\sqrt{3}$

Solution

Given,

$\lim_{x \to 3} \frac{\sqrt{3 x} - 3}{\sqrt{2 x - 4} - \sqrt{2}}$

On rationalization we get,

$\lim_{x \to 3} \frac{(3 x - 9) \times (\sqrt{2 x - 4} + \sqrt{2})}{\{(2 x - 4) - 2\} \times (\sqrt{3 x} + 3)}$

$= \lim_{x \to 3} \frac{3 (x - 3)}{2 (x - 3)} \times \frac{\sqrt{2 x - 4} + \sqrt{2}}{(\sqrt{3 x} + 3)}$

$= \frac{3}{2} \times \frac{2 \sqrt{2}}{6} = \frac{1}{\sqrt{2}} .$

Hence, the correct answer is option: 'A'.

limx→3⁡3x-32x-4- 2 is equal to

Solution

Relevant Questions

$\lim_{x \to 3} \frac{\sqrt{3 x} - 3}{\sqrt{2 x - 4} - \sqrt{2}}$ is equal to