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. 62222222,2,2zxyezxyexzyxyeFzyxzyxzyx2. 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).6109c. What is the minimum value of any directional derivative of f at the point (2, 1)? 6601d. 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 122yxz and above the region in the x- y plane between the curves 32xy 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),(22on 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!
View Full Document