Lim x - 5x2-9 x-20-x2-6 x-5

Lim_x → 5x^2 9x+20/x^2 6x+5 =lim_x → 5x^2 4x 5x+20/x^2 x 5x+5 =lim_x → 5x(x 4) 5(x 4)/(x 1) 5(x 1) =lim_x → 5(x 5)(x 4)/(x 5)(x 1) =lim_x → 5x 4/x 1 =5 4/5 1 =1 ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 5x2-9...

Question

${lim}_{x \to 5} \frac{x^{2} - 9 x + 20}{x^{2} - 6 x + 5}$

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Solution

${lim}_{x \to 5} \frac{x^{2} - 9 x + 20}{x^{2} - 6 x + 5}$

$= {lim}_{x \to 5} \frac{x^{2} - 4 x - 5 x + 20}{x^{2} - x - 5 x + 5}$

$= {lim}_{x \to 5} \frac{x (x - 4) - 5 (x - 4)}{(x - 1) - 5 (x - 1)}$

$= {lim}_{x \to 5} \frac{(x - 5) (x - 4)}{(x - 5) (x - 1)}$

$= {lim}_{x \to 5} \frac{x - 4}{x - 1}$

$= \frac{5 - 4}{5 - 1}$

$= \frac{1}{4}$

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(2002)

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limx→5x2−9x+20x2−6x+5

limx→5x2−9x+20x2−6x+5 =limx→5x2−4x−5x+20x2−x−5x+5 =limx→5x(x−4)−5(x−4)(x−1)−5(x−1) =limx→5(x−5)(x−4)(x−5)(x−1) =limx→5x−4x−1 =5−45−1 =14

${lim}_{x \to 5} \frac{x^{2} - 9 x + 20}{x^{2} - 6 x + 5}$