BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.3, Problem 24E
To determine

To sketch: The function y=cosx by hand without plotting any points and then graph the function y=|cosπx|.

Expert Solution

Explanation of Solution

The standard graph of the function y=cosx is roughly drawn and shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.3, Problem 24E , additional homework tip  1

Then, draw the graph of y=cosπx by compressing the graph y=cosx horizontally by π units. Thus, the graph of y=cosπx is shown below in Figure 2.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.3, Problem 24E , additional homework tip  2

From Figure 2, it is observed that Figure 1 is shrunken horizontally by a factor of π units.

Now, to draw the graph of y=|cosπx|, reflect the entire part of the graph y=cosπx that appears below the x-axis about the origin. Thus, the graph of y=|cosπx| is shown below in Figure 3.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.3, Problem 24E , additional homework tip  3

Observe that Figure 3 is obtained from Figure 1 in such a way that it is horizontally compressed by a factor of π units and then reflected the portions appeared below the x-axis about the x-axis.

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