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: 6

Answer

a. $\displaystyle \lim_{x\rightarrow 2}F(x)=4,\\$ b. $\displaystyle \lim_{x\rightarrow-1}F(x)=4$

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, ----------- ( F is not defined for x=2) a. As $x$ approaches 2 from either the left or right, $F(x)$ gets closer to 4. Both one-sided limits exist, and are equal, $\displaystyle \lim_{x\rightarrow 2}F(x)=4$ b. As $x$ gets closer to $-1$ from left or right, $F(x)$ gets closer to 4. Both one-sided limits exist, and are equal, $\displaystyle \lim_{x\rightarrow-1}F(x)=4$
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