Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.9 - Linearization and Differentials - Exercises 3.9 - Page 175: 32

Answer

a.0.4641 b.0.4 c the approximation of error =0.0641

Work Step by Step

as x.=1,dx=0.1 x.+dx=1+0.1 =1.1 as given formula in part a =1.1^4 -1^4 =1.4641-1 =0.4641 b. df/dx=4x^3 df=4(1)^3 * dx df=4*0.1 df=0.4 c. the approximation error =I0.4641-0.4I =0.0641
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