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← JEE Main 2017 · 8 Apr · Shift 1
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JEE Main 2017 · 8 Apr · Shift 1, Mathematics question 70

lim⁡x→33x−32x−4−2\displaystyle\lim_{x\to3}\frac{\sqrt{3x}-3}{\sqrt{2x-4}-\sqrt2} is equal to :

Choose one option
Answer and worked solution

Official answer: B

Rationalise both:
3(x−3)3x+3⋅2x−4+22(x−3)→36⋅222=12.\frac{3(x-3)}{\sqrt{3x}+3}\cdot\frac{\sqrt{2x-4}+\sqrt2}{2(x-3)}\to\frac36\cdot\frac{2\sqrt2}2=\frac1{\sqrt2}.

Topics:Limits
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