Lim x - 5x3-125-x2-7 x-10

Lim_x → 5x^3 125/x^2 7x+10 It is of the form 0/0 =lim_x → 5(x 5)(x^2+5x+25)/(x 2)(x 5) [ a^3 b^3=(a b); (a^2+ab+b^3) ] =(5)^2+25+5(5)/(5 2)=25+25+14/3=75/3=25 ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 5x3-1...

Question

${lim}_{x \to 5} \frac{x^{3} - 125}{x^{2} - 7 x + 10}$

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Solution

${lim}_{x \to 5} \frac{x^{3} - 125}{x^{2} - 7 x + 10}$

It is of the form $\frac{0}{0}$

$= {lim}_{x \to 5} \frac{(x - 5) (x^{2} + 5 x + 25)}{(x - 2) (x - 5)}$

$[\begin{matrix} a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{3}) \end{matrix}]$

$= \frac{(5)^{2} + 25 + 5 (5)}{(5 - 2)} = \frac{25 + 25 + 14}{3} = \frac{75}{3} = 25$

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limx→5x3−125x2−7x+10

limx→5x3−125x2−7x+10 It is of the form 00 =limx→5(x−5)(x2+5x+25)(x−2)(x−5) [a3−b3=(a−b)(a2+ab+b3)] =(5)2+25+5(5)(5−2)=25+25+143=753=25

${lim}_{x \to 5} \frac{x^{3} - 125}{x^{2} - 7 x + 10}$