2220hw7

2220hw7 - Math 2220 Problem Set 7 Spring 2010 Section 1.7...

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Unformatted text preview: Math 2220 Problem Set 7 Spring 2010 Section 1.7 : 20. (a) Graph the curve in R 2 having polar equation r = 2 a sin θ where a is a positive constant. (b) Graph the surface in R 3 having spherical equation ρ = 2 a sin ϕ . 22. Graph the surface whose spherical equation is ρ = 1- sin ϕ . 34. Sketch the solid whose spherical coordinates ( ρ, ϕ, θ ) satisfy 0 ≤ ρ ≤ 2 / cos ϕ , 0 ≤ ϕ ≤ π/ 4. Section 5.5 : 8. Consider the integral integraldisplay 1 integraldisplay ( y/ 2)+2 y/ 2 (2 x- y ) dx dy . (a) Evaluate the integral and sketch the region D of integration in the xy-plane. (b) Let u = 2 x- y and v = y . Find the region D * in the uv-plane that corresponds to D . (c) Use the change of variables theorem to evaluate the integral using the substitution u = 2 x- y , v = y . 10. Use a change of variables to determine the value of integraldisplayintegraldisplay D radicalbigg x + y x- 2 y dA where D is the region in R 2 enclosed by the lines y = x/ 2, y = 0, and x + y = 1....
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2220hw7 - Math 2220 Problem Set 7 Spring 2010 Section 1.7...

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