Evaluate-limx - 2x2-4-3x-2-x-2

Lim_x → 2x^2 4√(3x 2) √(x+2) lim_x → 2x^2 4√(3x 2) √(x+2)×(√(3x 2)+√(x+2)√(3x 2)+√(x+2)) lim_x → 2(x 2)(x+2)(√(3x 2)+√(x+2))(√(3x 2))^2 (√(x+2))^2 lim_x → 2x ...

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Byju's Answer

Standard XII

Mathematics

Vectorial Representation of a Complex Number

Evaluate:limx...

Question

Evaluate:

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

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Solution

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

${lim}_{x \to 2} \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}} \times (\frac{\sqrt{3 x - 2} + \sqrt{x + 2}}{\sqrt{3 x - 2} + \sqrt{x + 2}})$

${lim}_{x \to 2} \frac{(x - 2) (x + 2) (\sqrt{3 x - 2} + \sqrt{x + 2})}{(\sqrt{3 x - 2})^{2} - (\sqrt{x + 2})^{2}}$

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

${lim}_{x \to 2} \frac{(x + 2) (\sqrt{3 x - 2} + \sqrt{x + 2})}{2}$

$= \frac{4 (2 + 2)}{2}$

$= 8$

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Vectorial Representation of a Complex Number

Standard XII Mathematics

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Evaluate: limx→2x2−4√3x−2−√x+2

limx→2x2−4√3x−2−√x+2 limx→2x2−4√3x−2−√x+2×(√3x−2+√x+2√3x−2+√x+2) limx→2(x−2)(x+2)(√3x−2+√x+2)(√3x−2)2−(√x+2)2 limx→2x2−4√3x−2−√x+2 limx→2(x+2)(√3x−2+√x+2)2 =4(2+2)2 =8

Evaluate:

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