Calculus 8th Edition

We know that $\lim\limits_{x \to a}\frac{x^{n}-a^{n}}{x-a}= na^{n-1}$ By the theorem above, $\lim\limits_{x \to 1}\frac{x^{1000}-1^{1000}}{x-1}$ = $1000×1^{999}$ = 1000