Question

Evaluate the limit : $\underset{x\to -1}{lim}\frac{x^3+1}{x+1}$

Answer 1

Given: $\underset{x\to -1}{lim}\frac{x^3+1}{x+1}becomes\frac{0}{0}form$

Using Factorization method

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

$\Rightarrow \underset{x\to -1}{lim}\frac{(x+1)(x^2-x+1^2)}{x+1}$

$\Rightarrow \underset{x\to -1}{lim}(x^2-x+1)=\left(\right(-1{)}^2-(-1)+1)$

$=(1+1+1)=3$

Therefore,

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