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Unformatted text preview: April, 2006 MATH 105 Name Page 2 of 10 pages Marks  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. (a) Assume that z ( x, y ) is a linear function with slope 2 in the x-direction and slope − 3 in the y-direction. If z (1 , 1) = 4, find z ( − 2 , 1). Answer: (b) If f ( x, y ) = ln( x 2 + y ), find lim k → f (1 + k, 0) − f (1 , 0) k . Answer: (c) Let ( x , y ) be a critical point of f ( x, y ) = − x 2 − y 2 + 6 x + 8 y − 21. Find ( x , y ) and then find the equation of the tangent plane to the surface f ( x, y ) at the point ( x , y , f ( x , y ) ) . Answer: (d) Suppose the marginal revenue in producing x units of a certain product is MR ( x ) = 300 − . 2 x . Find the change in total revenue if production is increased from 10 to 20 units. Answer: Continued on page 3 April, 2006 MATH 105 Name Page 3 of 10 pages (e) Find Z 1 + x x − x 2 dx ....
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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 The University of British Columbia.
- Winter '10