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Review ProblemsMTH (Exam 3) - MTH203 Review Problems EXAM-3...

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Unformatted text preview: MTH203 Review Problems_( EXAM-3) / ' 1) Set up triple integral in cyliderical coordinates to find the volume of the solid that lies inside the graphs of both x2 + y2 +22=16 and x2 +y2 — 4y = 0. 2) Let R be the solid region bounded byz = 10 —x2 —y2 artdz=x2 +y2—8. Set upa triple integral for the volume of R. - 3) Find theetvolume of the wedge-shaped region enclosed on the side by the cylinder x = —cos(y). —7r/2 S y s ”/2, on the top by the plane 2 = —2x, below by the xy-plane 4)Set up triple integral in cylindrical coordinate for the integral I” ‘le + y2 + 2xy + z3 dV, Q is the first octant bounded by the cylinder x2 +y2 = 4 and Q the planes 2 = 0 and z = 4. 5) Set up triple integral in spherical coordinates for the integral [4]. 1H2 JET—fl e‘("2+y’+zz>dzdydx. 0 —J 16—):2 —1/16—Jr2--y2 6) For the vector field F(x, y) = xi +xyj, compute the line integral I Eat ;where C is V C the part of the circle r=5 joining the point (5,0) to the point (0,—5) in the counterclockwise direction. 7) Answer the following for the vector field F(x, y) a) Show that F is conservative b) Find a potential function f(x,y) such that V f = F. 0) Evaluate I F.d ; where C is any smooth path from (0,2) to (2,1). C 8) Evaluate f ydx —xdy + ydz, where C is the line segment connecting the point =< x—xy2,3 —x2y > C (-2,0, l) to the point (1,1,2). 9) Apply Greens Theorem to find f Re! ; where C F(x,y) = 3xyi + 2xj and C is the boundary of the region bounded by the line y = x and the parabola y = x2. . 10) Find work in two ways: Find the work done by F = (75% over the plane curve r(t) = (e’cos(t))i + (e‘sin(t))j from the point (1,0) to the point (e2”,0) in two ways: a) By using the parametrization of the curve to evaluate the work integral b) By evaluating a potential function for F. ...
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