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1. ### Calculus area element help

hm...interesting, I'll definitely be doing more problems for practice. Thanks
2. ### Calculus area element help

so do i just substitute all of those equations into x^2yz and take the derivatives once in respect to u and then once in respect to v?
3. ### Calculus area element help

Homework Statement Let f(x,y,z)=x^2yz. Express f*dA in terms of u and v. The Attempt at a Solution We're given that x= u+v y= u-v z= u^2+v^2. The main problem I'm having is that I know I need to take partial derivatives in respect to u and v but I'm not sure how. I did an easier...
4. ### Jacobian matrix with 2 variables

what do you mean? the determinant doesn't necessarily have to be a certain numerical value, just show what the answer is symbolically(that's what I believe atleast heh). so if I did this right the determinant should be just 2x+3x^2
5. ### Jacobian matrix with 2 variables

jacobian matrix with 2 variables please help! Homework Statement so we have z=x^2+x^3 and z=y+sin(x). Find the jacobian matrix of this system. Find the determinant of this jacobian. The Attempt at a Solution The determinant part is easy, the only problem is trying to set this up. I'm...
6. ### Calculus 3: Show Intersection of Tetrahedron Vertices & Centers of Gravity

hm...ok...i'll look into it. thanks
7. ### Calculus 3: Show Intersection of Tetrahedron Vertices & Centers of Gravity

well there would be four lines all crossing at the center of gravity and I'm suppose to show that with vectors though because this is a vector problem. I know the physics concept of it(learned it last semester) but I need to show it with vectors. Do you have any ideas?
8. ### Calculus 3: Show Intersection of Tetrahedron Vertices & Centers of Gravity

Well we show that the lines going from one vertice to the center of gravity of opposite sides will end up crossing each other right in the middle of the tetrahedron(the very center). The problem says that at that point, we know the answer is (P+Q+R+S)/4 where the letters correspond to vertices...
9. ### Calculus 3: Show Intersection of Tetrahedron Vertices & Centers of Gravity

That can't be right, we just barely started this class and we're only learning about vectors and haven't done anything with integration :bugeye:
10. ### Calculus 3: Show Intersection of Tetrahedron Vertices & Centers of Gravity

Homework Statement So we're suppose to show that the intervals connecting vertices of a tetrahedron with centers of gravity of opposite sides interesect at one point, namely the center of gravity of a normal tetrahedron. The center of gravity is (P+Q+R+S)/4. Homework Equations All I...