University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Practice Exercises - Page 474: 46


$n \geq 26$

Work Step by Step

The error bound for the Trapezoidal Rule is given as follows: $|E_T| \leq \dfrac{M(b-a)^3}{12n^2}$ Now, the maximum value of $|f^{2}(x)|$ on $[0,1]$ is: $M=8$ Further, $|E_T| \leq \dfrac{8(1-0)^3}{12n^2}=\dfrac{2}{3n^4}$ we will choose $n$ such that $\dfrac{2}{3n^2} \leq 10^{-3}$ Therefore, $n \geq 25.8 \approx 26$ Thus $n \geq 26$
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