Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.1 - Derivatives of Polynomials and Exponential Functions - 3.1 Exercises: 1

Answer

The number $e$ is defined as: $\lim\limits_{h \to 0} \frac{e^h - 1}{h}=1$. $\lim\limits_{h \to 0}\frac{2.7^{h}-1}{h} = 0.99$ $\lim\limits_{h \to 0}\frac{2.8^{h}-1}{h} = 1.03$ The value of $e$ is between 2.7 and 2.8.

Work Step by Step

The number $e$ is defined as: $\lim\limits_{h \to 0} \frac{e^h - 1}{h}=1$. $\lim\limits_{h \to 0}\frac{2.7^{h}-1}{h} = 0.99$ $\lim\limits_{h \to 0}\frac{2.8^{h}-1}{h} = 1.03$ You can find these values by using the table feature on a graphing calculator and finding values that are close to zero. The value of $e$ is between 2.7 and 2.8 since the above limits are around 1.
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