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

1 answer:

6 0

Do L'hospital's rule.

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

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