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exam 2 Solutions - Name Math 211A Fall 2005 Exam 2 Honor...

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Name: Math 211A Fall 2005 Exam # 2 Honor Code Write and sign the honor code here after you have finished the exam. There will be no calculators allowed during the exam. You may use a 3x5 inch note card. Use full sentences on all explanations and put a box around your final answer. Good Luck!! 1. True or False (2 points each) a. False The graph of r ( u, v ) = < cos u, cos v, sin( uv ) > is a space curve. b. True D u f = f · u . c. False If ρ ( x, y ) is the density of a lamina R at the point ( x, y ), then the center of mass of R is given by R ρ ( x, y ) dA . d. True A solution of LaPlace’s equation is called a harmonic function. e. False The graph of the function f ( x, y, z ) = x 2 + y 2 - z is a 1 dimensional object in 3 dimensional space.
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2. (10 points) Calculate lim ( x,y ) (0 , 0) y 2 x 2 + y 2 + sin 2 x y 2 + sin 2 x . If the limit does not exist, explain why. If the limit does exist, show why it converges to your answer. If x = 0 then lim ( x,y ) (0 , 0) y 2 x 2 + y 2 + sin 2 x y 2 + sin 2 x = lim y 0 0 + y 2 + 0 y 2 + 0 = 1.
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