Evaluate lim x - 2x2-4-3 x-2-x-2

=x → 2lim{(x^2 4)/√(3x 2) √(x+2)} =x → 2lim{(x^2 4)/√(3x 2) √(x+2)×(√(3x 2)+√(x 2))/(√(3x 2)+√(x 2))} =x → 2lim{(x^2 4)(√(3x 2)+√(x 2))/(3x 2) (x+2)} =x → 2lim{ ...

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Byju's Answer

Standard XI

Mathematics

Factorization Method Form to Remove Indeterminate Form

Evaluate lim ...

Question

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

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Solution

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

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

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

$= l i m x \to 2 \frac{(x + 2) (\sqrt{3 x - 2} + \sqrt{x - 2})}{2} [c a n c e l l i n g (x - 2)]$

$= 8 [p u t t i n g x = 2]$

Suggest Corrections

Evaluate limx→2{(x2−4)√3x−2−√x+2}

=limx→2{(x2−4)√3x−2−√x+2} =limx→2{(x2−4)√3x−2−√x+2×(√3x−2+√x−2)(√3x−2+√x−2)} =limx→2{(x2−4)(√3x−2+√x−2)(3x−2)−(x+2)} =limx→2{(x2−4)(√3x−2+√x−2)2(x−2)} =limx→2(x+2)(√3x−2+√x−2)2 [cancelling(x−2)] =8 [putting x=2]

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