The value of limx-2 x2-43x-2-x-2 is

Limx→2 nbsp;x2 43x 2 x+2=limx→2 nbsp;x2 43x 2 x+2×3x 2+x+23x 2+x+2=limx→2 nbsp;x2 43x 2+x+23x 22 x+22 nbsp; nbsp;00 nbsp;form=limx→2 nbsp;x 2x+23x ...

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Standard XII

Mathematics

Factorization

The value of ...

Question

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

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Solution

$lim x \to 2 \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}} = lim x \to 2 \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}} \times \frac{\sqrt{3 x - 2} + \sqrt{x + 2}}{\sqrt{3 x - 2} + \sqrt{x + 2}} = lim x \to 2 \frac{(x^{2} - 4) (\sqrt{3 x - 2} + \sqrt{x + 2})}{{(\sqrt{3 x - 2})}^{2} - {(\sqrt{x + 2})}^{2}} (\frac{0}{0} f o r m) = lim x \to 2 \frac{(x - 2) (x + 2) (\sqrt{3 x - 2} + \sqrt{x + 2})}{3 x - 2 - x - 2} (\frac{0}{0} f o r m) = lim x \to 2 \frac{(x - 2) (x + 2) (\sqrt{3 x - 2} + \sqrt{x + 2})}{2 x - 4} (\frac{0}{0} f o r m) = lim x \to 2 \frac{(x - 2) (x + 2) (\sqrt{3 x - 2} + \sqrt{x + 2})}{2 (x - 2)} (\frac{0}{0} f o r m) = lim x \to 2 \frac{(x + 2) (\sqrt{3 x - 2} + \sqrt{x + 2})}{2} = \frac{(2 + 2) (\sqrt{3 \times 2 - 2} + \sqrt{2 + 2})}{2} = 8$

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