Question: 3. The functions u and v are given by the following expressions: x+y - u= ; v= X (i) Find the Jacobian (u,v) (x,) (ii)

3. The functions u and v are given by the following expressions: x+y - u= ; v= X (i) Find the Jacobian (u,v) (x,) (ii) Comment if u and v are independent. (iii) If they are not independent, find the relationship between u and v. 4. (i) What property does the vector field F(x, y, z) possess for it to be a conservative field? (ii) Determine the value of C which will make the field F(x, y), given below a conservative field. F(x,y) = (Vx + 3xy)i + (Cx? + 4y)j (iii) Determine the potential function

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