Lim x - 21-x-2-4-x3-2 x2

Lim_x → 2 ( 1/x 2 4/x^3 2x^2 ) =lim_x → 2 ( 1/x 2 4/x^2(x 2) ) =lim_x → 21/x 2 [ 1/1 4/x^2 ] =lim_x → 2 ( x^2 4/x^2(x 2) ) [It is of (0/0) form] =lim_x → 2(x 2) ...

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Byju's Answer

Standard XII

Mathematics

Expansions to Remove Indeterminate Form

lim x → 21/x-...

Question

${lim}_{x \to 2} (\frac{1}{x - 2} - \frac{4}{x^{3} - 2 x^{2}})$

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Solution

${lim}_{x \to 2} (\frac{1}{x - 2} - \frac{4}{x^{3} - 2 x^{2}})$

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

$= {lim}_{x \to 2} \frac{1}{x - 2} [\frac{1}{1} - \frac{4}{x^{2}}]$

$= {lim}_{x \to 2} (\frac{x^{2} - 4}{x^{2} (x - 2)})$ [It is of $(\frac{0}{0})$ form]

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

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

$= \frac{(2 + 2)}{2^{2}} = \frac{4}{4}$

=1

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Similar questions

{lim}_{x \to 2} [\frac{1}{x - 2} - \frac{4}{x^{3} - {2 x}^{2}}]

Q. Find the limits :

i .

lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

i i .

lim x \to 2 [\frac{x^{3} - 4 x^{2} + 4 x}{x^{2} - 4}]

i i i .

lim x \to 2 [\frac{x^{2} - 4}{x^{3} - 4 x^{2} + 4 x}]

i v .

lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

lim x \to 1 [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}]

lim x \to \infty \frac{x^{3} + x^{2} + 1}{2 x^{2} + 3 x + 4}

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

Q. Solve

lim x \to 2 f (x) = lim x \to 2 \frac{(x^{2} - 4)}{(x - 2)}

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limx→2(1x−2−4x3−2x2)

limx→2(1x−2−4x3−2x2) =limx→2(1x−2−4x2(x−2)) =limx→21x−2[11−4x2] =limx→2(x2−4x2(x−2)) [It is of (00) form] =limx→2(x−2)(x+2)x2(x−2) [It is of (00) form] =limx→2(x+2)x2 =(2+2)22=44 =1

${lim}_{x \to 2} (\frac{1}{x - 2} - \frac{4}{x^{3} - 2 x^{2}})$