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mmatest - verify the answer on the graph ± 6 Define a...

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Mathematica test Steven Tschantz 2/15/11 Questions This is an open book, open computer test. Complete the following questions. You are to work individually in class for approximately one hour. Honor code provisions apply. Email your final version to [email protected] 1. Edit this file to put your name below the title above. 2. Define the symbol pilist to be a list of 4 numbers approximating the number Π : an integer, an exact rational number not an integer, a floating point decimal number, and the Mathematica symbol representing the exact value. Evaluate Sin[pilist] and explain the result you get. Evaluate pilist numerically to display decimal values for your numbers. 3. Find the derivative of exp I sin I log H x LMM with respect to x . 4. Find the area above the x -axis and under the curve y = cos I Π x 2 M + x - 1 between x = 0 and 1. 5. In the range 0 £ x £ 10, on the same graph, plot the line y = 2 x - 1 and the parabola y = x 2 - 7 x + 5. Solve for the intersection points of these curves, evaluating the results numerically so that you can
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Unformatted text preview: verify the answer on the graph. ± 6. Define a function f H x L = a + b x + c x . Find the coefficients a , b , and c such that f I 1 M = 1, f I 2 M = 1.2, and f I 3 M = 1.5. ± 7. Find where the minimum value of e x-x 3 + x occurs for 0 £ x £ 5. Plot the function and check you have found a minimum. ± 8. Define a linear demand function such that the demand at price p = 10. is a quantity q = 2000. and such that the demand has an elasticity at this price of Ε = ¶ q ¶ p p q = -2.5. ± 9. Assuming the above demand and a constant, but unspecified, marginal cost mc, write down the condition that should be satisfied for a monopoly firm supplying this demand at a price p to be profit maximizing. ± 10. Suppose that p = 10. is in fact the profit maximizing price. Determine what the marginal cost of the firm must be....
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