For each of the following vector fields F , decide whether it is conservative or

Question

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, f = F). If it is not conservative, type N. F (x, y) = (10x + 1y)i + (lx + 2y)j f (x,y) = F (x, y) = 5yi + 6xj f (x,y) = F (x, y, z) = 5xi + 6yj + k f(x,y,z) = F (x, y) = (5 sin y) i + (2y + 5x cos y) j f(x,y) = F (x, y, z) = 5x2i + 1y2j + 1z2k f(x,y,z) = Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"

Explanation / Answer

a) 5x2 + xy + y2

b) N

c) 2.5x2 + 3y2 + z

d) 5x siny + y2

e) (5x3 + y3 + z3)/3

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