a.
To verify: the given function
Yes, the function is nonnegative.
Given information:
The given function is
Concept Used:
Nonnegative function: It has function values equal to or greater than zero
Calculation:
First, draw the function
The graph is shown below:
From the above graph, it is observed that the function is above the
Therefore, the function is nonnegative at the given interval.
b.
To determine: the value of LRAM, RRAM and average approximations for the area under the graph of the function from
10 | 107.76 | 132.96 | 120.36 |
20 | 113.79 | 126.39 | 120.09 |
50 | 117.49 | 122.53 | 120.01 |
100 | 121.26 | 121.26 | 121.26 |
Given information:
The given function is
Concept Used:
Calculation:
The graph is shown below:
Here,
Now, use the LRAM program formula
The graph is shown below:
Now, use the RRAM program formula
Now, find the average approximation of the area by finding the average of LRAM and RRAM.
Use the above procedure to evaluate the
10 | 107.76 | 132.96 | 120.36 |
20 | 113.79 | 126.39 | 120.09 |
50 | 117.49 | 122.53 | 120.01 |
100 | 121.26 | 121.26 | 121.26 |
c.
To compare: the average area estimates in part (b) using 100 approximating rectangles with calculator NINT area estimate
The area from using 100 approximating rectangles is not equal to the NINT area.
Given information:
The given function is
Concept Used:
The notation
Calculation:
The graph is shown below:
The table is shown below:
10 | 107.76 | 132.96 | 120.36 |
20 | 113.79 | 126.39 | 120.09 |
50 | 117.49 | 122.53 | 120.01 |
100 | 121.26 | 121.26 | 121.26 |
Here,
The area from using 100 approximating rectangles is not equal to the NINT area.
Chapter 11 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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