Lim x -3x2-3-x2-3 -3 x-12

Lim_x →√(3)x^2 3/x^2 +3√(3)x 12 =lim_x →√(3)(x √(3))(x+√(3))/x^2+4√(3x) √(3x) 12 =lim_x →√(3)(x √(3))(x+√(3))/x(x+4√(3)) √(3)(x+4√(3)) =lim_x →√(3)(x √(3))(x+√ ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Limits

lim x →√3x2-3...

Question

${lim}_{x \to \sqrt{3}} \frac{x^{2} - 3}{x^{2} + 3 \sqrt{3} x - 12}$

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Solution

${lim}_{x \to \sqrt{3}} \frac{x^{2} - 3}{x^{2} + 3 \sqrt{3} x - 12}$

$= {lim}_{x \to \sqrt{3}} \frac{(x - \sqrt{3}) (x + \sqrt{3})}{x^{2} + 4 \sqrt{3 x} - \sqrt{3 x} - 12}$

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

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

$= \frac{\sqrt{3} + \sqrt{3}}{\sqrt{3} + 4 \sqrt{3}} = \frac{2 \sqrt{3}}{5 \sqrt{3}}$

$= \frac{2}{5}$

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Similar questions

Q. The value of

lim x \to \sqrt{3} \frac{x^{2} - 3}{x^{2} + 3 \sqrt{3} x - 12}

is equal to?

Q. Evaluate the following:

\begin{matrix} {lim}_{x \to 1} \frac{x^{2} - 3 x + 2}{x^{2} - 4 x + 3} {lim}_{x \to 2} \frac{x^{3} + x^{2} - 12}{x^{3} - x^{2} - x - 2} {lim}_{x \to \sqrt{2}} \frac{x^{2} + x \sqrt{2} - 4}{x^{2} - 3 x \sqrt{2} + 4} {lim}_{x \to 3} \frac{x^{3} - 3 x^{2} - x + 3}{x^{3} - 6 x^{2} + 9 x} \end{matrix}

\lim_{x \to 3} (\frac{1}{x - 3} - \frac{3}{x^{2} - 3 x})

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

\lim_{x \to 1} \frac{x^{3} + 3 x^{2} - 6 x + 2}{x^{3} + 3 x^{2} - 3 x - 1}

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limx→√3x2−3x2+3√3x−12

limx→√3x2−3x2+3√3x−12 =limx→√3(x−√3)(x+√3)x2+4√3x−√3x−12 =limx→√3(x−√3)(x+√3)x(x+4√3)−√3(x+4√3) =limx→√3(x−√3)(x+√3)(x−√3)(x+4√3) =√3+√3√3+4√3=2√35√3 =25

${lim}_{x \to \sqrt{3}} \frac{x^{2} - 3}{x^{2} + 3 \sqrt{3} x - 12}$