The value of Limx - 2x2-4-3 x-2-x-2 is

The correct option is C 8x→ 2limx^2 4/√(3x 2) √(x+2) =x→ 2lim(x^2 4)(√(3x 2)+√(x+2))/(3x 2) (x+2) =x→ 2lim(x+2)(̸x̸ ̸2̸)̸ (√(3x 2)+√(x+2))/2̸(̸x̸ ̸2̸)̸ =(2+ ...

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Question

The value of $L i m x \to 2 \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}}$ is

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Solution

The correct option is D 8
$l i m x \to 2 \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}} = l i m x \to 2 \frac{(x^{2} - 4) (\sqrt{3 x - 2} + \sqrt{x + 2})}{(3 x - 2) - (x + 2)} = l i m x \to 2 \frac{(x + 2) / (x - 2) (\sqrt{3 x - 2} + \sqrt{x + 2})}{/ 2 (x - 2)} = \frac{(2 + 2) (\sqrt{3 \times 2 - 2} + \sqrt{2 + 2})}{2} = \frac{4 \times 4}{2} = 8$ .

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Similar questions

Evaluate $l i m x \to 2 {\frac{(x^{2} - 4)}{\sqrt{3 x - 2} - \sqrt{x + 2}}}$

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lim x \to 2 \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}}

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The value of Limx→2x2−4√3x−2−√x+2 is

The correct option is D 8limx→2x2−4√3x−2−√x+2=limx→2(x2−4)(√3x−2+√x+2)(3x−2)−(x+2)=limx→2(x+2)/(x−2)(√3x−2+√x+2)/2(x−2)=(2+2)(√3×2−2+√2+2)2=4×42=8.

The value of $L i m x \to 2 \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}}$ is