# The graph of f ( x ) which satisfies the conditions, lim x → 0 − f ( x ) = 2 , lim x → 0 + f ( x ) = 0 , lim x → 4 − f ( x ) = 3 , lim x → 4 + f ( x ) = 0 , f ( 0 ) = 2 and f ( 4 ) = 1 . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 2.2, Problem 16E
To determine

## To sketch: The graph of f(x) which satisfies the conditions, limx→0−f(x)=2,limx→0+f(x)=0, limx→4−f(x)=3,limx→4+f(x)=0,f(0)=2 and f(4)=1.

Expert Solution

### Explanation of Solution

Graph:

Given that, limx0f(x)=2,limx0+f(x)=0,limx4f(x)=3,limx4+f(x)=0,f(0)=2 and f(4)=1.

Here, the left hand limit and the right hand limit of limx0f(x) and limx4f(x) are not the same.

Hence, the limits, limx0f(x) and limx4f(x) does not exist.

Moreover, according to the given conditions the graph must contain two points such that (0, 2) as f(0)=2 and (4, 1) as f(4)=1.

Thus, the possible graph of f(x) is shown below in Figure 1. In Figure 1, open dots indicate that the points are excluded.

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