Question

Evaluate lim→−1x^10 + x^3 + 1 / x-1​

Answer 1

The limand is continuous at x = -1, so

$\displaystyle\lim_{x\to-1}\frac{x^{10}+x^3+1}{x-1}=\frac{(-1)^{10}+(-1)^3+1}{-1-1}=-\dfrac{1-1+1}2=-\dfrac12$