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MATH 252 TEST 3 SPRING, 2004Remember to keep your work neat and orderly. Show all of your work. NO WORK = NO CREDIT! Read each question carefully and be sure to answer the question that was asked. Good luck!Name:____________________________________________________________ pts1. If zxyezyxFzyx22),,( , find F. 62222222,2,2zxyezxyexzyxyeFzyxzyxzyx2. Let 523),(32 yxxyxfa. Find the derivative of f in the direction given by the angle 43 (measured from thepositive x-axis). 6)643(21223yxxy b. Find the derivative of f in the direction of the vector v<3, -1> at the point (2, 1).6109c. What is the minimum value of any directional derivative of f at the point (2, 1)? 6601d. Find the equation of the plane that is tangent to the surface of ),( yxfz  at the point (2,1,3). 60)3()1(24)2(5  zyx3. Set up (do not evaluate) two different iterated integrals that will evaluate the area between the curves 22xy  and xy 2. 12   dydxdxdyAyyyxxxxy    8022/4022/24. Set up (do not evaluate) an iterated integral that will evaluate the volume of the solid that lies below the surface 122yxz and above the region in the x- y plane between the curves 32xy and 211 xy . 10dxdyyxVxx 22113122225. Find the integral of the function yxyxf 63),(  over the region R, if R is the area in the third quadrant that lies between the two circles centered at the origin with radii of 1 and 2. Evaluate completely. 12= -216. Evaluate completely: dxdyeyx 4014/2(Change the order of integration). 10=2e - 27. Find all critical points of the function 223227),( yxyxxyxf . 10)15,2(),152(),0,3(),0,3( 8. Find the absolute maximum and absolute minimum of the function yyxxyxf 42),(22on the region bounded by the lines x = 0, y = 3, and x = 2y (a triangle with vertices (0,0), (0,3), and (6,3)). You do not need to give the x-y points where the extremum occur, but you must show allthe points that you checked. 14Abs max = 21; abs min = -5 only crit pt is (1,2)9. What would you like us to cover in class next week? Any reasonable answer gets 2 points!


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SCSU MAT 252 - MATH 252 TEST 3

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