Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.1 - Exponential Functions - Exercise Set - Page 451: 82

Answer

See graph and explanations.
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Work Step by Step

a. We can graph $y=e^x$ (red) with $y=1+x+\frac{x^2}{2}$ (blue) as shown in the figure. b. We can add $y=1+x+\frac{x^2}{2}+\frac{x^3}{6}$ (green) to the graph. c. We can add $y=1+x+\frac{x^2}{2}+\frac{x^3}{6}+\frac{x^4}{24}$ (purple) to the graph. d. We can see that with an increasing number of terms in the polynomial, we get a better approximation to the function $y=e^x$ Extra: as a matter of fact, the polynomials used in the graph are the first few terms of the Taylor expansion of the function $y=e^x$
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