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# DiffCalculus: September 19, 2012

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### DiffCalculus: September 19, 2012

1. 1. 1. Limits - In action
2. 2. 1. Limits - In actionWith a string of 1 meter, construct a rectangle withthe largest area possible.
3. 3. 1. Limits - In action1. Draw a picture that represents the situation. Listthe known data and label the base of the rectangleas “x”.
4. 4. 1. Limits - In action1. Draw a picture that represents the situation. Listthe known data and label the base of the rectangleas “x”.
5. 5. 1. Limits - In action1. Draw a picture that represents the situation. Listthe known data and label the base of the rectangleas “x”. 1m
6. 6. 1. Limits - In action1. Draw a picture that represents the situation. Listthe known data and label the base of the rectangleas “x”. 1m
7. 7. 1. Limits - In action1. Draw a picture that represents the situation. Listthe known data and label the base of the rectangleas “x”. 1m P=1m
8. 8. 1. Limits - In action1. Draw a picture that represents the situation. Listthe known data and label the base of the rectangleas “x”. 1m P=1m x
9. 9. 1. Limits - In action2. Find the height as a function of the base of therectangle.Suggestion: Use the formula of the perimeter of arectangle and the value of the perimeter given inthe problem.
10. 10. 1. Limits - In action3. Write the area, A, as a function of the base ofthe rectangle and simplify the resulting expression.
11. 11. 1. Limits - In action4. Find the limit
12. 12. 1. Limits - In action5. Set the resulting expression equal to zero andsolve the equation.
13. 13. 1. Limits - In action6. Using a graphing software, sketch the graph ofA.
14. 14. 1. Limits - In action6. Using a graphing software, sketch the graph ofA.
15. 15. 1. Limits - In action7. Using the graph, find the value obtained in step5.What is special about this point?You can build your rectangle!