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13 Nov 2019
o Math Qulz 15: 15.8-16.3 (Take-Home) All work must be clearly shown for partial credit 1. Evaluate the integral by changing to cylindrical coordinates. (5 pts) x2+y dz dy dr 2. Consider the transformation T: x -2u+3v y 3u+2v a) Sketch the image of S under T of the unit square R-{(u,v) 0susl, Osvs in the uv- plane using the change of coordinates. b) Evaluate (3x+ 2y A (5 pts) 3. Evaluate Jx'yd -xdy where C is the circlex+y-1 with counterclockwise orientation. (5 pts 4. Evaluate F-dr where F(x,ya) (+ 3yi+3j+ xyk and C is given by (5 pts 5. Show that F(x.y) - sin yi + (xcos y + sin y)j is a conservative vector field and find a function f such that F -vf (5 pts 8. Show that F(x.y) (2x+y'+3'yi+ (2xy'+3y')i is a conservative vector field and use his fact to evaluate IF-dr where C sthe arc of the an er(t)-(vsin) OstsÏ (5 pts
o Math Qulz 15: 15.8-16.3 (Take-Home) All work must be clearly shown for partial credit 1. Evaluate the integral by changing to cylindrical coordinates. (5 pts) x2+y dz dy dr 2. Consider the transformation T: x -2u+3v y 3u+2v a) Sketch the image of S under T of the unit square R-{(u,v) 0susl, Osvs in the uv- plane using the change of coordinates. b) Evaluate (3x+ 2y A (5 pts) 3. Evaluate Jx'yd -xdy where C is the circlex+y-1 with counterclockwise orientation. (5 pts 4. Evaluate F-dr where F(x,ya) (+ 3yi+3j+ xyk and C is given by (5 pts 5. Show that F(x.y) - sin yi + (xcos y + sin y)j is a conservative vector field and find a function f such that F -vf (5 pts 8. Show that F(x.y) (2x+y'+3'yi+ (2xy'+3y')i is a conservative vector field and use his fact to evaluate IF-dr where C sthe arc of the an er(t)-(vsin) OstsÏ (5 pts
Patrina SchowalterLv2
8 Jun 2019