Vecotrs 08 - MATH 3012 - FINAL EXAM December 12, 2008...

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Unformatted text preview: MATH 3012 - FINAL EXAM December 12, 2008 Question 1. ((1) Find the equation of the plane that contains the point P(1,—1,—2) and is parallel to the plane 31' — 5y + 22 = 2. ( b) Find the equation of a line (any line you want) that contains the point P(1,—1,—2) and is parallel to the plane 31' — 5y + 22 = 2. Question 2. Decide if the following limit exists or not: hm my cos(y) - (I,y)—>(0,0) 21:2 —— 2312 Question 3. Compute the iterated integral by first reversing the order of integration: 1 1 112 / / x63 dydx. 0 fi 11 ///Ede where E is bounded by the planes y = 0, z = [Lx + y = 2 and the cylinder 312 + 22 = 1 in the first octant. Question 4. Compute Question 5. Use Green’s Theorem to evaluate f ny dx — x112 dy C where C is the circle x2 + 312 = 4. Question 6. (a) Parametrize the surface y = x2 + 22. (b) Compute the surface integral //55dS where S is the part of the paraboloid y = x2 + 22 that lies inside the cylinder 2:2 + 22 = 4. Question 7. Compute the surface area of the sphere of radius 1. //SF-dS where F(x, y, z) = x -j — z - k and S is the part of the paraboloid z = 2:2 +312 below the plane 2 = 3 with upward orientation. /F~d7‘ C where F(x,y) = x2 - i — my -j and C is a quarter of the circle 2:2 + 3/2 = 1 from (—1,0) to (0, —1). Question 8. Evaluate Question 9. Compute Question 10. Evaluate the integral // 6(2+y)/(2—y)dA R where R is the trapezoidal region with vertices (1, 0), (2, 0), (0, —2) and (0, —1). Use the change of variables: u+v u—v x = . ...
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Vecotrs 08 - MATH 3012 - FINAL EXAM December 12, 2008...

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