Answer
1000
Work Step by Step
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
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 144: 107
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