Math 2231 – Project Ch 4 Name: _______________________________
| Project Component |
Points Earned |
| Part 1 – Rectangle Approximations: Left Endpoints |
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| a) Approximations Chart on Page 1 is filled out accurately |
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|
2 |
1 |
0 |
| b) Accurate numerical approximation for n = 3 |
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|
|
1 |
0 |
| c) Accurate numerical approximation for n = 6 |
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|
|
1 |
0 |
| d) Accurate numerical approximation for n = 12 |
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|
2 |
1 |
0 |
| e) Graph with colored rectangles is correctly created using Desmos for n = 3 and n = 12 |
|
3 |
2 |
1 |
0 |
| f) Exact area is correctly calculated using Limit definition |
4 |
3 |
2 |
1 |
0 |
| g) Comparison of approximations as n increases |
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|
|
1 |
0 |
| h) Error is calculated for n = 3, n = 6, and n = 12 |
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1 |
0 |
| Part 2 – Trapezoidal Rule and Simpson’s Rule |
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| a) Accurate numerical approx. using Trapezoidal Rule for n = 4 |
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2 |
1 |
0 |
| b) Correct graph with trapezoids is constructed |
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|
2 |
1 |
0 |
| c) Exact area is correctly calculated using Fundamental Theorem |
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|
2 |
1 |
0 |
| d) Accurate numerical approximation using Simpson’s Rule for n = 4 |
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|
2 |
1 |
0 |
| Part 3 – Excel file |
|
| a) Accurate left endpoint approximations for all values of n |
4 |
3 |
2 |
1 |
0 |
| b) Accurate right endpoint approximations for all values of n |
4 |
3 |
2 |
1 |
0 |
| c) Accurate midpoint approximations for all values of n |
|
3 |
2 |
1 |
0 |
| d) Accurate approximations for all values of n – Trapezoid Rule |
|
3 |
2 |
1 |
0 |
| e) Accurate approximations for all values of n – Simpson Rule |
|
|
2 |
1 |
0 |
| Project Organization |
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| Work is clear and organized & pages are submitted in the correct order |
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|
|
1 |
0 |
TOTAL POINTS AVAILABLE: 40 TOTAL POINTS FOR THIS PROJECT: _______