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Unformatted text preview: Math 215 Fall 2011 Exam 2 Name: Lab section: Instructions: • The exam consist of 7 problems for a total of 100 points. Please look through the exam booklet and make sure it has twelve pages. The next to last page is a list of formulas which may be useful. The last page is blank and is to be used as scratch paper. You may tear both of those pages apart from the rest of the exam. • The exam duration is 90 minutes. • No calculators are allowed. • Make sure your answers are clearly marked (circled or boxed). Points Possible Problem 1 12 Problem 2 12 Problem 3 12 Problem 4 12 Problem 5 20 Problem 6 20 Problem 7 12 Total 100 Problem 1 (12 points): The volume of a cylinder is given by V = πr 2 h , where r is the radius of the cylinder and h is the height. The surface area of the same cyliner is given by A = 2 πr 2 + 2 πrh . Suppose we want to construct a cylinder that has volume 250 π cm 3 and has the least surface area possible. Use the method of Lagrange multipliers to determine what the dimensions of the cylinder should be. Problem 2 (12 pts.):3030 4 4 8 8 6 6 16 16 224 12 12 Consider the function f ( x, y ), whose level curves are shown above. Call the shaded rectangular region D . Assume that each hash mark on the coordinate axes represents an integer. Consider the following integrals: integraldisplay 1 1 integraldisplay 3 5 f ( x, y ) dx dy , integraldisplay 5 3 integraldisplay 1 / 2 f ( x, y ) dy dx , integraldisplayintegraldisplay D f ( x, y ) dA....
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 Fall '08
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 Calculus, Formulas, ice cream, Polar coordinate system

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