limx→33x-32x-4-2 is equal to:

limx→33x-32x-4-23x+33x+32x-4+22x-4+2 = limx→33x-92x-4-22x-4+23x+3 =limx→33(x-3)2(x-3)2x-4+23x+3 =32226=12

limx→33x-32x-4-2 is equal to:

limx→33x-32x-4-23x+33x+32x-4+22x-4+2 = limx→33x-92x-4-22x-4+23x+3 =limx→33(x-3)2(x-3)2x-4+23x+3 =32226=12

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

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

$\frac{1}{2 \sqrt{2}}$

$\frac{1}{\sqrt{2}}$

$\sqrt{3}$

answer is C.

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Detailed Solution

$\lim_{x \to 3} \frac{\sqrt{3 x} - 3}{\sqrt{2 x - 4} - \sqrt{2}} \frac{\sqrt{3 x} + 3}{\sqrt{3 x} + 3} \frac{\sqrt{2 x - 4} + \sqrt{2}}{\sqrt{2 x - 4} + \sqrt{2}} = \lim_{x \to 3} \frac{3 x - 9}{2 x - 4 - 2} \frac{\sqrt{2 x - 4} + \sqrt{2}}{\sqrt{3 x} + 3} = \lim_{x \to 3} \frac{3 (x - 3)}{2 (x - 3)} \frac{\sqrt{2 x - 4} + \sqrt{2}}{\sqrt{3 x} + 3} = \frac{3}{2} \frac{2 \sqrt{2}}{6} = \frac{1}{\sqrt{2}}$