MAT-2130 Final: MATH 2130 App State Fall2013 Final Exam
Document Summary
Be sure to show your work: (12 points) let f(x, y, z) = h2y + yz2, 2x + xz2 + 1, 2xyz + 3z2i. (a) compute zc. F dr where c is the line segment from ( 1, 0, 1) to (2, 1, 1). To parameterize the line segment from point p to point q we can use: r(t) = p + (q p )t where 0 t 1. So in particular, we have: r(t) = h 1, 0, 1i +h2 ( 1), 1 0, 1 1it = h 1 + 3t, t, 1i where 0 t 1. 9t + 9t 2 dt = 9t2 2t(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) 2x + xz2 + 1 2xyz + 3z2. Z p dx =z 2y + yz2 dx = 2xy + xyz2 + c1(y, z) Z r dz =z 2xyz + 3z2 dz = xyz2 + z3 + c3(x, y)
