Question

evaluate
lim x --> 1 [(x^1000)-1]/[x-1]

Answer 1

Do L'hospital's rule.

$\lim_{x \to 1} \frac{x^{1000}-1}{x-1}= \lim_{x \to 1} \frac{(x^{1000}-1)'}{(x-1)'}= \lim_{x \to 1} \frac{1000x^{999}}{1}= \\ \\ \frac{1000\times1^{999}}{1}=\frac{1000}{1}=1000$