Question

Evaluate the given limit :
$\underset{x\to -1}{lim}\frac{(x^{10}+x^5+1)}{x-1}$

Answer 1

Given : $\underset{x\to -1}{lim}\frac{x^{10}+x^5+1}{x-1}$
Substituting $x=-1$
$=\frac{(-1{)}^{10}+(-1{)}^5+1}{(-1)-1}$
$=\frac{1-1+1}{-1-1}$
$=\frac{0+1}{-2}$
$=-\frac{1}{2}$
$\therefore$ $\underset{x\to -1}{lim}\frac{x^{10}+x^5+1}{x-1}=-\frac{1}{2}$