Evaluate the limit - limx- 3 1x-3-2x2-4x-3

Given: lim_x→ 3 ( 1x 3 2x^2 4x+3 ) becomes ∞ ∞ form nbsp; Using Factorization method =lim_x→ 3 ( 1x 3 2x^2 4x+3 ) =lim_x→ 3 ( x^2 4x+3 2(x 3)(x 3)(x^2 4 ...

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Standard XIII

Mathematics

Rationalization Method to Remove Indeterminate Form

Evaluate the ...

Question

Evaluate the limit : $lim x \to 3 (\frac{1}{x - 3} - \frac{2}{x^{2} - 4 x + 3})$

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Solution

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

becomes $\infty - \infty$ form

Using Factorization method

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

$= lim x \to 3 (\frac{x^{2} - 4 x + 3 - 2 (x - 3)}{(x - 3) (x^{2} - 4 x + 3)})$

$= lim x \to 3 (\frac{x^{2} - 4 x + 3 - 2 x + 6}{(x - 3) (x^{2} - 4 x + 3)})$

$= lim x \to 3 (\frac{x^{2} - 6 x + 9}{(x - 3) (x^{2} - 4 x + 3)})$

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

$= lim x \to 3 (\frac{(x - 3)}{x (x - 3) - 1 (x - 3)})$

$= lim x \to 3 (\frac{(x - 3)}{(x - 3) (x - 1)})$

$= lim x \to 3 (\frac{1}{x - 1}) = \frac{1}{3 - 1} = \frac{1}{2}$

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

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Similar questions

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

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

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$(i i i) {lim}_{x \to 0^{+}} \frac{1}{3 x}$

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$(v i i) {lim}_{x \to \frac{π}{2^{+}}} s e c x$

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Q. Evaluate the limit :

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

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Rationalization Method to Remove Indeterminate Form

Standard XIII Mathematics

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Evaluate the limit : limx→3(1x−3−2x2−4x+3)

Evaluate the limit : $lim x \to 3 (\frac{1}{x - 3} - \frac{2}{x^{2} - 4 x + 3})$