Question

Determine o limite LIM = (x^5-1) / (1-x^4)
x->1

Answer 1

$\underset{x\to1}{\lim}\frac{x^5-1}{1-x^4}=\underset{x\to1}{\lim}\frac{(x-1)(x^4+x^3+x^2+x+1)}{-(x-1)(x+1)(x^2+1)}=\underset{x\to1}{\lim}\frac{(x^4+x^3+x^2+x+1)}{-(x+1)(x^2+1)}=$ $\frac{((1)^4+(1)^3+(1)^2+(1)+1)}{-((1)+1)((1)^2+1)}=\frac{1+1+1+1+1}{-(1+1)(1+1)}=\frac{5}{-(2)(2)}=-\frac54$