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M105Mar23RevisedSampleLiu09

M105Mar23RevisedSampleLiu09 - April 2009 MATH 105 Name Page...

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Unformatted text preview: April, 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) The level curve of the function f ( x,y ) = x 2 + y 2 containing the point (1 , 2) is a circle. Find the radius of the circle. Answer: (b) Compute ∂f ∂y ( π, 2) if f ( x,y ) = cos x y . Answer: (c) Find all point(s) ( x,y ) where f ( x,y ) = x 2- 2 xy- y 2 + 12 x- 1 has a possible relative maximum or minimum. Answer: (d) If f ( x,y ) = ln(2 x- 3 y ), find lim h → f ( x + h,y )- f ( x,y ) h . Answer: Continued on page 3 April, 2009 MATH 105 Name Page 3 of 10 pages (e) If the marginal cost of producing x units of a product A is given by MC ( x ) = 0 . 3 x 2 +2 x and the fixed cost is $2000, find the cost of producing 20 units of the product A . Answer: (f) Find Z ln(5 x ) x dx . Answer: (g) Find Z sin- 1 xdx . Answer: (h) Find the volume of the solid of revolution obtained from revolving the region below the graph of y = e- x from x = 0 to x = 1. Answer: Continued on page 4 April, 2009 MATH 105 Name Page 4 of 10 pages (i) Given the demand function p = D ( x ) = 50 e- . 05 x , find the average price over the demand interval [10 , 30]. Answer: (j) Given that 6 Z 3 p 2 f ( x ) dx = 5, what is 6 Z 3 p f ( t ) dt ? Answer: (k) Find an integrating factor for the differential equation y + √ ty = 2( t + 1), t > 0....
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M105Mar23RevisedSampleLiu09 - April 2009 MATH 105 Name Page...

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