Question

Lim x---1

X³-1
___
X-1

Answer 1

$\mathrm{\lim\limits_{x\to1}\dfrac{x^3-1}{x-1}=\lim\limits_{x\to1}\dfrac{(x-1)(x^2+x+1)}{x-1}=}\\\\ \mathrm{=\lim\limits_{x\to1}(x^2+x+1)=1^2+1+1=1+2=\boxed{\mathbf{3}}}$