Lim x - 3x2-x-6-x3-3 x2-x-3

Lim_x → 3x^2 x 6/x^3 3x^2+x 3 ( 0/0form ) =lim_x → 3x^2 3x+2x 6/x^2(x 3)+1(x 3) =lim_x → 3x(x 3)+2(x 3)/(x 3)(x^2+1) =lim_x → 3(x 3)(x+2)/(x 3)(x^2+1) =lim_x → ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 3x2-x...

Question

${lim}_{x \to 3} \frac{x^{2} - x - 6}{x^{3} - 3 x^{2} + x - 3}$

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Solution

${lim}_{x \to 3} \frac{x^{2} - x - 6}{x^{3} - 3 x^{2} + x - 3} (\frac{0}{0} f o r m)$

$= {lim}_{x \to 3} \frac{x^{2} - 3 x + 2 x - 6}{x^{2} (x - 3) + 1 (x - 3)}$

$= {lim}_{x \to 3} \frac{x (x - 3) + 2 (x - 3)}{(x - 3) (x^{2} + 1)}$

$= {lim}_{x \to 3} \frac{(x - 3) (x + 2)}{(x - 3) (x^{2} + 1)}$

$= {lim}_{x \to 3} \frac{x + 2}{x^{2} + 1} = \frac{3 + 2}{(3)^{2} + 1} = \frac{5}{10}$

$= \frac{1}{2}$

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limx→3x2−x−6x3−3x2+x−3

limx→3x2−x−6x3−3x2+x−3(00form) =limx→3x2−3x+2x−6x2(x−3)+1(x−3) =limx→3x(x−3)+2(x−3)(x−3)(x2+1) =limx→3(x−3)(x+2)(x−3)(x2+1) =limx→3x+2x2+1=3+2(3)2+1=510 =12

${lim}_{x \to 3} \frac{x^{2} - x - 6}{x^{3} - 3 x^{2} + x - 3}$