Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 10 - Section 10.1 - Limits: Numerical and Graphical Viewpoints - Exercises - Page 701: 52

Answer

See below.

Work Step by Step

We either draw the graph by hand or graph using technology. Placing a pencil on the graph left of the line $x=a$ and tracing rightward towards $x=a$, we record the $y$-coordinates of the points of the graph. If the $y$-values approach approach a number $L_{1}$, we estimate $L_{1}$ as the left limit of the function at $x=a$. If they don't, we conclude that there is no left limit. Similarly, from the right side of the graph, we either estimate $L_{2}$, the right limit, or we conclude that there is none. If both one-sided limits exist and the equal the same number $L$, we say that $L$ is the limit of the function at $x=a$. One disadvantage is that we may not be able to PRECISELY determine the limit.
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