amal2002

Determine which of the following vector fields F in the plane is the gradient of a scalar function f. If such an f exists, find it. F(x,y) = (cos xy-xysin xy)-(x2 sin xy)? F(x,y)= (2? cos y+ cos y??(x2siny4 ? siny)) a. b.

(3) For each of the following vector fields, g : R2 → R, determine whether it may be a gradient. If so, find a scalar field f such that? g. (a) g(x,y) = (y,-x) (b) g(x,y) = (5x4 + y, x-12y3) (c) g(x,y) = (3x2 cos y,-x? siny) (d) g(x, y ) = (eg see x, eg tan x) (e) g(x, y) = (xy,-y) (f) g(x,y) = (x2+y, cos y)