Lim x - 3x2-4 x-3-x2-2 x-3

Lim_x → 3x^2 4x+3/x^2 2x 3 It is of the form 0/0 lim_x → 3x^2 3x x+3/x^2+x 3x 3 =lim_x → 3x(x 1) 3(x 1)/x(x+1) 3(x+1) =lim_x → 3(x 1)(x 3)/(x+1)(x 3) =lim_x → 3 ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 3x2-4...

Question

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

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Solution

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

It is of the form $\frac{0}{0}$

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

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

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

$= {lim}_{x \to 3} \frac{x - 1}{x + 1}$

$= \frac{3 - 1}{3 + 1}$

$= \frac{2}{4} = \frac{1}{2}$

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limx→3x2−4x+3x2−2x−3

limx→3x2−4x+3x2−2x−3 It is of the form 00 limx→3x2−3x−x+3x2+x−3x−3 =limx→3x(x−1)−3(x−1)x(x+1)−3(x+1) =limx→3(x−1)(x−3)(x+1)(x−3) =limx→3x−1x+1 =3−13+1 =24=12

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