Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 3 - The Derivative - 3.1 Limits - 3.1 Exercises: 7

Answer

a. 0 b. does not exist

Work Step by Step

The graph consists of points (x,f(x)). When inspecting limits at x=a, approach a on the x axis and observe what happens to the y-coordinate, f(x), on the graph. A limit exists only if both one-sided limits exist, and are equal, ----------- Note: $f(0)=2, f(2)=-2\\$ a. As $x$ approaches $0$ from the left or from the right, $f(x)$ gets closer to $0$. Both one-sided limits exist, and are equal, $\displaystyle \lim_{x\rightarrow 0}f(x)=0$ b. As $x$ approaches 2 from the left, $f(x)$ gets closer to $-2$. As $x$ approaches 2 from the right, $f(x)$ gets closer to 1. Both one-sided limits exist, but are NOT equal, $\displaystyle \lim_{x\rightarrow 2}f(x)$ does not exist.
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