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: 33

Answer

a.-3^-1 b.-0.4 c.The approximation error is = 0.0667

Work Step by Step

x.=0.5,dx=0.1 x.+dx=0.5+0.1 =0.6 a.use in given formula =f(x.+dx)-f(x.) =0.6^-1 - 0.5^-1 =-3^-1 b.df/dx=? df/dx=-x^-2 =-(0.5)^-2*dx =-4*0.1 =-0.4 c. the approximation error=? =I-3^-1 -(-0.4)I =I-3^-1 + 0.4I =0.06666666667 =0.0667
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