Math_105_April_2009

Math_105_April_2009 - Marks[42 1 MATH 105 Name Page 2 of 10...

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April 27, 2009 MATH 105 Name Page 2 of 10 pages Marks [42] 1. Short-Answer Questions . Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. At most one mark will be given for incorrect answers. (a) Compute ∂f ∂x (2 , 1) if f ( x, y ) = e (1 - x ) y . Answer: (b) Let f ( x, y ) = (2 x + y 3 ) 10 . Evaluate 2 f ∂y∂x . Answer: (c) Find all point(s) ( x, y ) where f ( x, y ) = x 2 + y 2 + xy +3 x - 7 may have a relative maximum or minimum. Answer: (d) Find the value of k that makes the following antidifferentiation formula true: Z 7 5 - 2 x dx = k ln | 5 - 2 x | + c, where c is a constant. Answer: Continued on page 3
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April 27, 2009 MATH 105 Name Page 3 of 10 pages (e) Suppose that the marginal revenue function for a company is 500 - 3 x 2 . Find the addi- tional revenue received from doubling production if currently 5 units are being produced. Answer: (f) Find Z x - 2 ( x 2 - 4 x + 7) 2 dx . Answer: (g) Find Z 5 x sin( x + 1) dx . Answer: (h) Use the trapezoidal rule with n = 3 to approximate Z 3 0 dx 1 + x 3 . Answer: Continued on page 4
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April 27, 2009 MATH 105 Name Page 4 of 10 pages (i) Find the volume of the solid of revolution generated by revolving about the x -axis the region under the graph of y = x 3 / 2 from x = 0 to x = 2. Answer: (j) Find the area under the graph of y = e - 2 x for x 0. Answer: (k) Find the consumer’s surplus for the demand curve p = 25 - 0 . 03 x 2 at the sale level x = 10.
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