Question

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

Answer 1

Do L'hospital's rule.


`\lim_(x \to 1) (x^(1000)-1)/(x-1)= \lim_(x \to 1) ((x^(1000)-1)')/((x-1)')= \lim_(x \to 1) (1000x^(999))/(1)= \\ \\ (1000*1^(999))/(1)=(1000)/(1)=1000`