Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.2 - The Natural Exponential Function - 4.2 Exercises - Page 341: 20

Answer

(a) See the image below.

Work Step by Step

As we can see on the image $y=e$ is a line (a number) which the graph of $y=(1+\frac{1}{x})^x$ approaches "infinitely" close but not actually gets to it. We also have a term for it which is $Asymptote$ (Also explained in later chapters). In this case we have $Horizontal Asymptote$. In short $e$ is a limit (*also explained later in calculus) of the function $f(x)=(1+\frac{1}{x})^x$ as $x$ approaches infinity.
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