Math_200_December_2008

Math_200_December_2008 - Math 200, Final Exam December 2008...

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Math 200, Final Exam December 2008 No calculators or notes of any kind are allowed. Time: 2.5 hours. 1. [11] Asur faceisg ivenby z = x 2 2 xy + y 2 . (a) Find the equation of the tangent plane to the surface at x = a, y =2 a. (b) For what value of a is the tangent plane parallel to the plane x y + z =1 ? 2. [12] The pressure in a solid is given by P ( s, r )= sr (4 s 2 r 2 2) where s is the speci f cheatand r is the density. We expect to measure ( s, r ) to be approximately (2 , 2) and would like to have the most accurate value for P. There are two di f erent ways to measure s and r . Method 1 has an error in s of ± 0 . 01 andanerrorin r of ± 0 . 1 , while method 2 has an error of ± 0 . 02 for both s and r . Should we use method 1 or method 2? Explain your reasoning carefully. 3. [11] u ( x, y ) is de f ned as u ( x, y )= e y F ( xe y 2 ) for an arbitrary function F ( z )

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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.

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Math_200_December_2008 - Math 200, Final Exam December 2008...

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