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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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