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Unformatted text preview: April 27, 2009 MATH 105 Name Page 2 of 10 pages Marks [42] 1. ShortAnswer 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 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 dx 1 + x 3 . Answer: Continued on page 4 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 xaxis 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....
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This note was uploaded on 01/23/2011 for the course MATH 100,200,30 taught by Professor Dr.alejandrocortas during the Winter '10 term at UBC.
 Winter '10
 Dr.AlejandroCortas
 Math

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