exam 2 Solutions

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 Fnished 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 Fnal answer. Good Luck!! 1. True or ±alse (2 points each) a. ±alse The graph of r ( u,v )= < cos u, cos v, sin( uv ) > is a space curve. b. True D ±u f = f · . c. ±alse If ρ ( x,y ) is the density of a lamina R at the point ( ), then the center of mass of R is given by ±± R ρ ( ) dA . d. A solution of LaPlace’s equation is called a harmonic function. e. ±alse 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 =1. If y = 0 then lim ( x,y ) (0 , 0) y 2 x 2 + y 2 + sin 2 x y 2 + sin 2 x = lim x 0 0+0+sin 2 x 0 + sin 2 x =1 .
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This test prep was uploaded on 04/12/2008 for the course MATH 211 taught by Professor Crow during the Fall '07 term at Gettysburg.

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

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