Question: 1. A) Find a function f such that F = Vf and B) use part A) to evaluate S F. dr along the given curve

1. A) Find a function f such that F = Vf and B) use part A) to evaluate S F. dr along the given curve C. F(x, y, z) = 2xy z* i + 3x y z* j + 4xy z'k, C. x= t, y=?, z=t, Ost=2 2. Use Green's Theorem to evaluate the line integral along the given positively oriented curve. Se (y2 - tan 'x) dx + (3x + sin y) dy, C is the boundary of the region enclosed by the parabola y = x and the line y = 4 3. Evaluate the surface integral JJ F. dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = e'i+ ye'j + xlyk, S is the part of the paraboloid z = x' + y' that lies above the square 0

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