Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.4 Exercises - Page 81: 108

Answer

For the left-hand limit, we will be on the fourth piece which approaches $28$ as $t$ approaches $4$ and for the right-hand limit we will be on the fifth piece which approaches $56$ as $t$ approaches $4$. That is, $\lim_\limits{t \to 4^-}f(t)=28$ $\lim_\limits{t \to 4^+}f(t)=56$

Work Step by Step

Since, we are reducing the change in the $t$ from a different direction. We will be on different pieces of the graph in both the limits. Hence, for the left-hand limit, we will be on the fourth piece which approaches $28$ as $t$ approaches $4$ and for the right-hand limit we will be on the fifth piece which approaches $56$ as $t$ approaches $4$. That is, $\lim_\limits{t \to 4^-}f(t)=28$ $\lim_\limits{t \to 4^+}f(t)=56$
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