Recent content by twotwelve

Yes, thank you. I was actually inquiring if anyone could find a better way to represent the surface area.

Did I perhaps set something up wrong? Could this be parameterized somehow as an Elliptic Paraboloid?

Apostol page 429, problem 4 Is there a better way to set up this problem or have I made a mistake along the way? (ie easier to integrate by different parameterization) Homework Statement Find the surface area of the surface z^2=2xy lying above the xy plane and bounded by x=2 and y=1...

\begin{facepalm*} that makes it about a 2 second proof then \end{facepalm*} -thanks

Apostol page 386, problem 5 Homework Statement Given f,g continuously differentiable on open connected S in the plane, show \oint_C{f\nabla g\cdot d\alpha}=-\oint_C{g\nabla f\cdot d\alpha} for any piecewise Jordan curve C. Homework Equations 1. Green's Theorem 2. \frac{\partial...

Yes, I was heading in the wrong direction. My solution: Any points (x_0,y_0,z_0) meeting our conditions will also have orthogonal tangent planes at those points satisfying (x_0,y_0,z_0) \cdot (a-x_0,b-y_0,c-z_0)=0. However, they also satisfy both f and g. Solving for all three yields...

Hmm, after deliberating over this problem for a good bit of time, the most that I can figure is any sphere having radius 1 and intersecting with f must have a center within the outer sphere h:x^2+y^2+z^2=9. I know that the gradient vectors of f are all orthogonal to f(x,y,z)=1. I also know...

Does this suggest that I should examine the intersection f-g? Or should I find \nabla f \cdot \nabla g? I am genuinely unclear...

Apostol 281, 4. Homework Statement Find the set of points (a,b,c) for which the spheres below intersect orthogonally. sphere 1: f(x,y,x):x^2+y^2+z^2=1 sphere 2: g(x,y,z):(x-a)^2+(y-b)^2+(z-c)^2=1 The Attempt at a Solution II know that the gradient vector, \nabla f, is normal...