Lim x - 1 x-2 x 2-x-1 x 3-3 x 2-2 x

Limx #8594;1x 2x2 x 1x3 3x2+2x=limx #8594;1x 2xx 1 1xx2 3x+2=limx #8594;1x 2xx 1 1xx2 2x x+2=limx #8594;1x 2xx 1 1xxx 2 1x 2 =limx #8594;1x 2xx 1 1xx ...

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Byju's Answer

Standard XII

Mathematics

Factorization

lim x → 1 x-2...

Question

$\lim_{x \to 1} \{\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}\}$

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Solution

$\lim_{x \to 1} [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}] = \lim_{x \to 1} [\frac{x - 2}{x (x - 1)} - \frac{1}{x (x^{2} - 3 x + 2)}] = \lim_{x \to 1} [\frac{x - 2}{x (x - 1)} - \frac{1}{x (x^{2} - 2 x - x + 2)}] = \lim_{x \to 1} [\frac{x - 2}{x (x - 1)} - \frac{1}{x \{x (x - 2) - 1 (x - 2)\}}]$
$= \lim_{x \to 1} [\frac{x - 2}{x (x - 1)} - \frac{1}{x (x - 1) (x - 2)}] = \lim_{x \to 1} [\frac{{(x - 2)}^{2} - 1}{x (x - 1) (x - 2)}]$

$= \lim_{x \to 1} [\frac{(x - 1) (x - 3)}{x (x - 1) (x - 2)}] = \frac{(1 - 3)}{1 (1 - 2)} = \frac{- 2}{- 1} = 2$

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limx→1 x-2x2-x-1x3-3x2+2x

limx→1x-2x2-x-1x3-3x2+2x=limx→1x-2xx-1-1xx2-3x+2=limx→1x-2xx-1-1xx2-2x-x+2=limx→1x-2xx-1-1xxx-2-1x-2 =limx→1x-2xx-1-1xx-1x-2=limx→1x-22-1xx-1x-2 =limx→1x-1x-3xx-1x-2=1-311-2=-2-1=2

$\lim_{x \to 1} \{\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}\}$