Recent content by MechanicalBrank

Sorry, didn't notice I wrote function, it's supposed to be vector field. I solved it anyhow so it's all good.

Silly me. Determine the line of force to the function F and if the function is conservative or not.

Homework Statement F(x,y) =(x2y,xy2) Homework EquationsThe Attempt at a Solution I wrote the function as a differential equation dy/x2y = dx/xy2. After integration I got C+y2=x2. This gave me that the line of force is a hyperbolic paraboloid. The function is not conservative. ∂F1/∂y = x2 ...

You have understood correctly. The problem asks to find the general equations for finding any potential maxima. I guess it means that they want me to create a general system of equations that would find the maxima if we were given a function. There's a subproblem after this one where they ask to...

Homework Statement Let u = ∂f/∂x and v = ∂f/∂y. Use Lagrange's method to set up the equations necessary for finding the maxium of u^2 + v^2. Homework EquationsThe Attempt at a Solution I know how to minimize and maximize a function that's a subject to another one. I'm not quite sure what the...

I think I solved it.

Let f(x,y)=x^2 + xy + y^2 for all x in R2. Find a parameterization of the curve given by the intersection of f(x,y) and the plane z=2x+y. That's the problem exactly as on paper.

Homework Statement f(x,y) = x^2 + xy + y^2 and z=2x+y intersect, find a parameterization of the curve where they intersect. Homework EquationsThe Attempt at a Solution I am lost. I know that z is the partial derivative of the original function, if that's of any use. I can visualize it but not...

Homework Statement D1 = {(x,y) : x^2 + y^2 < 3, x+2y = 2} D2={(x,y) : x^2 + y^2 > 2} D3={(x,y) : x + 2y = 2} Homework EquationsThe Attempt at a Solution D1 is neither, D2 is open and D3 is closed, am I right or wrong?