(b) If F(x, y) = (4x + 4y)i + (4x + 4y)j, then f(x, y) =

Let the vector C represents the coefficients of a polynomial pt=c1+c2t+c3t2+c4t3. Express the conditions p0=1, p'0=2, p1=1, p'1=0 in the form AC=b.

Determine whether each of the following vector fields F is path independent (conservative) or not. If it is path independent, enter a potential function for it, that is, a function f(x, y) so that Vf = F. If it is path dependent, enter NONE. (a) If F(x, y) = (x + 2)i + (3y + 4)j, then f(x, y) = (b) If F(x, y) = (4x + 5y)i + (5x + 2y)j, then f(x, y) = (C) If F (x, y) = (-2y, 2x), then f(x, y) = (d) If F(x, y) = (5æ² – y?, –2æy), then f(x, y) = (e) If F (x, y) = бу i + 6 In(x + 5)j, then a + 5 f(x, y) = (1) If F (x, y) = 4y sin(æy)i + 4x sin(æy)j, then f(x, y) =

Determine whether each of the following vector fields F is path independent (conservative) or not. If it is path independent, enter a potential function for it, that is, a function f(x, y) so that Vf = F. If it is path dependent, enter NONE.