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

Lim_x → 2 ( x/x 4 4/x^2 2x ) =lim_x → 2 ( x/x 2 4/x(x 2) ) =lim_x → 21/x 2 ( x/1 4/x ) =lim_x → 21/x 2 ( x^2 4/x ) =lim_x → 2 ( (x 2)(x+2)/x(x 2) ) =lim_x → 2(x ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 2x/x-...

Question

${lim}_{x \to 2} (\frac{x}{x - 2} - \frac{4}{x^{2} - 2 x})$

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Solution

${lim}_{x \to 2} (\frac{x}{x - 4} - \frac{4}{x^{2} - 2 x})$

$= {lim}_{x \to 2} (\frac{x}{x - 2} - \frac{4}{x (x - 2)})$

$= {lim}_{x \to 2} \frac{1}{x - 2} (\frac{x}{1} - \frac{4}{x})$

$= {lim}_{x \to 2} \frac{1}{x - 2} (\frac{x^{2} - 4}{x})$

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

$= {lim}_{x \to 2} \frac{(x + 2)}{x}$

$= \frac{2 + 2}{2}$

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

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limx→2(xx−2−4x2−2x)

limx→2(xx−4−4x2−2x) =limx→2(xx−2−4x(x−2)) =limx→21x−2(x1−4x) =limx→21x−2(x2−4x) =limx→2((x−2)(x+2)x(x−2)) =limx→2(x+2)x =2+22 =42=2

${lim}_{x \to 2} (\frac{x}{x - 2} - \frac{4}{x^{2} - 2 x})$