Calculus: Early Transcendentals 8th Edition

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

Chapter 1 - Section 1.4 - Exponential Functions - 1.4 Exercises: 6

Answer

(a) The number $e$ is defined as the base of the exponential function such that its slope at the point $(0,1)$ is exactly equal to $1$. (b) $e\approx2.718281828459\ldots$ (c) $$f(x)=e^x.$$

Work Step by Step

(a) The number $e$ is defined as the base of the exponential function $f(x)=e^x$ such that its slope at the point $(0,1)$ is exactly equal to $1$. (b) The approximate value of $e$ is $2.718281828459\ldots$ (c) The natural exponential function is the one with the basis equal to $e$: $$f(x)=e^x.$$
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