Lim x -3x4-9-x2-4 -3 x-15

A:lim_x →√(3)x^4 9/x^2+4√(3x) 15 lim_x →√(3)(x^2)^2 (3)^2/x^2+5√(3x) √(3x) 15 lim_x →√(3)(x^2 3)(x^2+3)/x(x+5√(3)) √(3)(x+5√(3)) lim_x →√(3)(x 3)(x+3)(x^2+3)/(x ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x →√3x4-9...

Question

${lim}_{x \to \sqrt{3}} \frac{x^{4} - 9}{x^{2} + 4 \sqrt{3 x} - 15}$

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Solution

$A : {lim}_{x \to \sqrt{3}} \frac{x^{4} - 9}{x^{2} + 4 \sqrt{3 x} - 15}$

${lim}_{x \to \sqrt{3}} \frac{(x^{2})^{2} - (3)^{2}}{x^{2} + 5 \sqrt{3 x} - \sqrt{3 x} - 15}$

${lim}_{x \to \sqrt{3}} \frac{(x^{2} - 3) (x^{2} + 3)}{x (x + 5 \sqrt{3}) - \sqrt{3} (x + 5 \sqrt{3})}$

${lim}_{x \to \sqrt{3}} \frac{(x - 3) (x + 3) (x^{2} + 3)}{(x - \sqrt{3}) (x + 5 \sqrt{3})}$

$= {lim}_{x \to \sqrt{3}} \frac{(x - \sqrt{3}) (x + \sqrt{3}) (x^{2} + 3)}{(x - \sqrt{3}) (x + 5 \sqrt{3})}$

$= {lim}_{x \to \sqrt{3}} \frac{(x + \sqrt{3}) (x^{2} + 3)}{(x + 5 \sqrt{3})}$

$= \frac{(\sqrt{3} + \sqrt{3})}{(\sqrt{3} + 5 \sqrt{3})} = \frac{(2 \sqrt{3}) (6)}{6 \sqrt{3}} = 2$

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limx→√3x4−9x2+4√3x−15

${lim}_{x \to \sqrt{3}} \frac{x^{4} - 9}{x^{2} + 4 \sqrt{3 x} - 15}$