University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 2 - Section 2.4 - One-Sided Limits - Exercises - Page 85: 20

Answer

(a) $\lim_{t\to4^+}(t-[t])=0$ (b) $\lim_{t\to4^-}(t-[t])=1$
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Work Step by Step

The graph is shown below. (a) $$\lim_{t\to4^+}(t-[t])$$ Looking at the graph, we see that as $t$ approaches $4$ from the right, $f(t)=t-[t]$ approaches $0$. Therefore, $$\lim_{t\to4^+}(t-[t])=0$$ (b) $$\lim_{t\to4^-}(t-[t])$$ Looking at the graph, we see that as $t$ approaches $4$ from the left, $f(t)=t-[t]$ approaches $1$. Therefore, $$\lim_{t\to4^-}(t-[t])=1$$
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