Ltx→aa+2x−3x3a+x−2x=

Using L-Hospital rule given limit is limx→a12a+2x(2)−123x(3)123a+x−212x=233

Ltx→aa+2x−3x3a+x−2x=

Using L-Hospital rule given limit is limx→a12a+2x(2)−123x(3)123a+x−212x=233

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$\underset{x \to a}{L t} \frac{\sqrt{a + 2 x} - \sqrt{3 x}}{\sqrt{3 a + x} - 2 \sqrt{x}} =$

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$\frac{2}{\sqrt{3}}$

$- \frac{1}{\sqrt{3}}$

$\frac{2}{3 \sqrt{3}}$

$\frac{1}{\sqrt{3}}$

answer is C.

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Detailed Solution

Using L-Hospital rule given limit is $\lim_{x \to a} \frac{\frac{1}{2 \sqrt{a + 2 x}} (2) - \frac{1}{2 \sqrt{3 x}} (3)}{\frac{1}{2 \sqrt{3 a + x}} - 2 \frac{1}{2 \sqrt{x}}} = \frac{2}{3 \sqrt{3}}$

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Ltx→aa+2x−3x3a+x−2x=

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$\underset{x \to a}{L t} \frac{\sqrt{a + 2 x} - \sqrt{3 x}}{\sqrt{3 a + x} - 2 \sqrt{x}} =$