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 2.2, Problem 14E
To determine

To sketch: The graph of f(x) which satisfies the conditions, limx0f(x)=1,limx3f(x)=2,limx3+f(x)=2, f(0)=1 and f(3)=1.

Expert Solution

Explanation of Solution

Graph:

Given that, limx0f(x)=1,limx3f(x)=2,limx3+f(x)=2, f(0)=1 and f(3)=1.

Here, the left hand limit and the right hand limit of limx3f(x) are not the same.

Hence, limx3f(x) does not exist.

Moreover, according to the given conditions the graph must contain two points such that (0, −1) as f(0)=1  and (3, 1) as f(3)=1.

Thus, the possible graph of f(x) is shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.2, Problem 14E

In Figure 1, open dots indicate that the points are excluded.

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