MATH 241 Midterm: MATH241H_HERB-R_FALL2003_0101_MID_SOL_2

• School: University of Maryland
• Department: Mathematics
• Course: MATH 241
• Professor: ALL

Document Summary

Math 241h - exam 3 - november 24, 2003 - solutions. Show your work: the paraboloids intersect when 9 r2 = 1 + r2 so that r = 2. Z z zw px2 + y2 dv = z 2 . 1+r2 r2 dz dr d = 256 /15: use green"s theorem with nx my = x2 + y2 and d the region inside the circle r = 3. Z zd x2 + y2 dxdy = z 2 . 0 r3 drd = 81 /2: do directly. F(x(t), y(t)) x (t) = (et, t3) (1, 2t) = et + 2t4. The answer is f (2, 1) f (0, 0) = e2 5/2: the surface is the part of the graph of z = x2 + y2 lying over the circle x2 + y2 5. Since q1 + f 2 x + f 2 y = p1 + 4x2 + 4y2, the surface area is.