MATH 0240 Final: MATH 240 Final Exam-51
Document Summary
Let f (x, y) = xy be de ned on the closed triangular region. T with vertices ( 1, 0), (1, 0), and (0, 1). Find the points on t where f has its absolute maximum and absolute minimum values, and nd these values. Let f (x, y, z) = zex/y, and x = u + v, y = uv2, z = v: find the gradient of f at the point (u, v) = (1, 1), calculate f. V and evaluate it at the point (u, v) = (1, 1). Let d be the region above the paraboloid z = 3 + x2 + y2 and below the paraboloid z = 11 x2 y2. F n ds, where f(x, y, z) =< 2x, 2y, 3z >, S is the boundary of d, and n is the outward unit normal vector to s. give a complete numerical answer.
