Lim x - 21-x-2-2-x2-2 x

Lim_x → 2 ( 1/x 2 2/x^2 2x ) =lim_x → 2 ( 1/x 2 2/x(x 2) ) [ lim_x → 21/(x 2) ( 1/1 2/x ) ] =lim_x → 2 ( x 2/(x 2)(x) ) [It is of (0/0) form] =lim_x → 21/x =1/ ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 21/x-...

Question

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

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Solution

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

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

$[{lim}_{x \to 2} \frac{1}{(x - 2)} (\frac{1}{1} - \frac{2}{x})]$

$= {lim}_{x \to 2} (\frac{x - 2}{(x - 2) (x)})$ [It is of $(\frac{0}{0})$ form]

$= {lim}_{x \to 2} \frac{1}{x}$

$= \frac{1}{2}$

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Similar questions

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Q. If

f (x) = {\begin{matrix} x^{2} + 2, & x \geq 2 1 - x, & x < 2 \end{matrix}

and

g (x) = {\begin{matrix} 2 x, & x > 1 3 - x, & x \leq 1 \end{matrix}

, then the value of

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is ............

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limx→2(1x−2−2x2−2x)

limx→2(1x−2−2x2−2x) =limx→2(1x−2−2x(x−2)) [limx→21(x−2)(11−2x)] =limx→2(x−2(x−2)(x)) [It is of (00) form] =limx→21x =12

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