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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Factorization Method Form to Remove Indeterminate Form

lim x →-1x3+1...

Question

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

Open in App

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

Suggest Corrections

Similar questions

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

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

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

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

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

Join BYJU'S Learning Program