Lim_x → 1x^3+1/x+1 =lim_x → 1(x+1)(x^2 x+1)/(x+1) [a^3+b^3=(a+b)(a^2+b^2 ab)] =lim_x → 1(x^2 x+1) =( 1)^2 ( 1)+1 =1+1+1 =3 ...

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Factorization Method Form to Remove Indeterminate Form

lim x →-1x3+1...

Question

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

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Solution

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

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

$[a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)]$

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

$= (- 1)^{2} - (- 1) + 1$

=1+1+1

=3

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