Lim x - 21 x-2-22 x-3 x 3-3 x 2-2 x

Limx #8594;21x 2 22x 3x3 3x2+2x=limx #8594;21x 2 22x 3xx2 3x+2=limx #8594;21x 2–22x 3xx2 2x x+2=limx #8594;21x 2 22x 3xxx 2 1x 2=limx #8594;21x 2 22x ...

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Byju's Answer

Standard XII

Mathematics

Factorization

lim x → 21 x-...

Question

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

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Solution

$\lim_{x \to 2} [\frac{1}{x - 2} - \frac{2 (2 x - 3)}{x^{3} - 3 x^{2} + 2 x}] = \lim_{x \to 2} [\frac{1}{x - 2} - \frac{2 (2 x - 3)}{x (x^{2} - 3 x + 2)}] = \lim_{x \to 2} [\frac{1}{x - 2} - \frac{- 2 (2 x - 3)}{x (x^{2} - 2 x - x + 2)}] = \lim_{x \to 2} [\frac{1}{x - 2} - \frac{2 (2 x - 3)}{x \{x (x - 2) - 1 (x - 2)\}}] = \lim_{x \to 2} [\frac{1}{x - 2} - \frac{2 (2 x - 3)}{x (x - 1) (x - 2)}] = \lim_{x \to 2} [\frac{x (x - 1) - 2 (2 x - 3)}{x (x - 1) (x + 2)}] = \lim_{x \to 2} [\frac{x^{2} - x - 4 x + 6}{x (x - 1) (x + 2)}] = \lim_{x \to 2} [\frac{x^{2} - 5 x + 6}{x (x - 1) (x + 2)}] = \lim_{x \to 2} [\frac{x^{2} - 2 x - 3 x + 6}{x (x - 1) (x - 2)}] = \lim_{x \to 2} [\frac{x (x - 2) - 3 (x - 2)}{x (x - 1) (x - 2)}] = \lim_{x \to 2} [\frac{(x - 3) (x - 2)}{x (x - 1) (x - 2)}] = \frac{2 - 3}{2 (2 - 1)} = - \frac{1}{2}$

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Similar questions

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

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

\lim_{x \to 2} (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x})

lim x \to 3 x^{3} - 3 x^{2} + x - 3

= ________

Q. Evaluate the following:

\begin{matrix} {lim}_{x \to 1} \frac{x^{2} - 3 x + 2}{x^{2} - 4 x + 3} {lim}_{x \to 2} \frac{x^{3} + x^{2} - 12}{x^{3} - x^{2} - x - 2} {lim}_{x \to \sqrt{2}} \frac{x^{2} + x \sqrt{2} - 4}{x^{2} - 3 x \sqrt{2} + 4} {lim}_{x \to 3} \frac{x^{3} - 3 x^{2} - x + 3}{x^{3} - 6 x^{2} + 9 x} \end{matrix}

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limx→2 1x-2-22x-3x3-3x2+2x

limx→21x-2-22x-3x3-3x2+2x=limx→21x-2-22x-3xx2-3x+2=limx→21x-2--22x-3xx2-2x-x+2=limx→21x-2-22x-3xxx-2-1x-2=limx→21x-2-22x-3xx-1x-2=limx→2xx-1-22x-3xx-1x+2=limx→2x2-x-4x+6xx-1x+2=limx→2x2-5x+6xx-1x+2=limx→2x2-2x-3x+6xx-1x-2=limx→2xx-2-3x-2xx-1x-2=limx→2x-3x-2xx-1x-2=2-322-1=-12

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