Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 9: 1

Answer

The solution is $r=9.8696$.

Work Step by Step

We need to solve the inequality $| r - \pi^{2} | < 10^{-4} $. That is, we have $ -10^{-4} \lt r - \pi^{2} \lt 10^{-4} $ $ -10^{-4} + \pi^{2}\lt r \lt 10^{-4} + \pi^{2} $ We know that $\pi$ is not a rational number and neither is $\pi^2$. So, we can not take the solution $r = \pi^2$ between $-10^{-4} + \pi^{2}$ and $10^{-4} + \pi^{2}$. But, as a close estimation of a rational number to the irrational number $\pi^2$, we can choose $r=9.8696$. Thus, the solution is $r=9.8696$.
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