ex3_fall11_2313 - Name: MAC 2313 Exam 3 Version A...

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Name: MAC 2313 Exam 3 Version A 10/05/2011 SHOW ALL YOUR WORK. Answers without procedure will be graded zero. [6] 1. Find and sketch the domain of f ( x,y ) = ln(2 x 2 + y 2 - 4) y - 5 [6] 2. Identify (i.e. write the corresponding equation/s) and sketch a contour map for f ( x,y ) = p 1 + y 2 - x , with k = 0 , 1 , 2
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[6] 3. Find the limit, if it exists, or show that the limit does not exist. a) lim ( x,y ) (1 , 0) ln ± 1 + y 2 x 2 + xy ² b) lim ( x,y ) (0 , 0) y 2 + sin 2 2 x 2 y 2 + 4 x 2 [6] 4. Find the following partial derivatives for f ( x,y ) = e xy cos( x ) sin( y ) a) Find f y ( x,y ) for f ( x,y ) = e xy cos( x ) sin( y ) b) Find f yx
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5. [4] a) Find an equation for the tangent plane to the surface given by f ( x,y ) = x 2 y at the point where ( x,y ) = (2 , - 1) [2] b) Use part a) to give the linear approximation of the surface at ( x,y ) = (2 . 5 , - 0 . 5). [6] Suppose you want to paint a closed box of square base with side 40cm and height 100 cm, use differentials to estimate the amount of paint if the layer of paint is 0.01 cm thick. (in cm
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ex3_fall11_2313 - Name: MAC 2313 Exam 3 Version A...

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