Question

Evaluate the following limit:
$\underset{x\to -1}{\text{lim}}\frac{x^{10}+x^5+1}{x-1}$

Answer 1

Here, $\underset{x\to -1}{\text{lim}}\frac{x^{10}+x^5+1}{x-1}$
= $\frac{(-1{)}^{10}+(-1{)}^5+1}{-1-1}=\frac{1-1+1}{-2}=\frac{-1}{2}$.