Question

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

Answer 1

At $x\to -1$,

$\frac{x^3+1}{x+1}$ becomes $\frac{0}{0}$ form

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

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

$=3(-1{)}^{3-1}[\because \underset{x\to a}{lim}\frac{x^n-a^n}{x-a}=n{a}^{n-1}]=3$