University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 2 - Section 2.3 - The Precise Definition of a Limit - Exercises - Page 75: 7

Answer

$\delta=0.1$

Work Step by Step

Find a $\delta\gt0$ such that for all $x$ $$0\lt (x-5)\lt\delta\Rightarrow|f(x)-6|\lt0.2$$ Looking at the graphs, we can see that for values of $f(x)$ to be restricted between $5.8$ and $6.2$ (which is $|f(x)-6|\lt0.2$), $x$ must be placed between $4.9$ and $5.1$. And since $5.1-5=0.1$, that means $0\lt (x-5)\lt0.1$. Therefore, $\delta=0.1$ (or any smaller positives number is also fine).
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