Calculus Concepts: An Informal Approach to the Mathematics of Change 5th Edition

Published by Brooks Cole
ISBN 10: 1-43904-957-2
ISBN 13: 978-1-43904-957-0

Chapter 1 - Ingredients of Change: Functions and Limits - 1.2 Activities - Page 21: 21


$\lim\limits_{x \to \infty}(1+\frac{1}{x})^{x}\approx2.718$

Work Step by Step

Numerical Estimation: For $x=1000$ ; $(1+\frac{1}{1000})^{1000}\approx2.71692$ For $x=10000$ ; $(1+\frac{1}{10000})^{10000}\approx2.71815$ For $x=100000$ ; $(1+\frac{1}{100000})^{100000}\approx2.71827$ For $x=1000000$ ; $(1+\frac{1}{1000000})^{1000000}\approx2.71828$ For $x=10000000$ ; $(1+\frac{1}{10000000})^{10000000}\approx2.71828$
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