Recent content by *Helix*

I'm going to work on it. my final solution is due monday morning :( ..so we'll see what i can come up with..I'll post very soon!

Well, I know the standard parametric form for when a hyperboloid is around the z axis. That is: x=a*cosh(u)*cos(v) y=b*cosh(u)*sin(v) z=c*sinh(u) v in this sense is between 0 and 2*PI and if a=b=c, then it is a circular type hyperboloid, with the apex in the xy plane as a circle..am I...

nice..thanks..I at least get this part! we let: v=x+y u=x-y w=z-u then w2 + v2 -u2 = 1 which we see is hyperboloid with an axis of symmetry around u?! anddd...expanding all that out in terms of x y and z, we get the original equation ...which is sweet so x = (v+u)/2 y =...

when I complete the square in z, assuming I have the right u and v now, I get z = -u plus or minus the square root of (u2 - v2 + 1) ..this is what I was getting before...hmmm

so I should end up with z2 +z(2u) + v2 = 1 ...right? And I'm to complete the square in z and use another varible?

well, using v and u in the equation, you end up with ( u^2 - v^2 + 1) which is (-4xy +1) under the radical...what happens to z??

Hi Dick, your suggestion looked goods, I have come up with the following, I just need a little help with grasping how the parameters work. let me know what you think of this solution so far: if we let u = x - y v = x + y then: u2 = x2 - 2xy + y2 Substituting the change of varibles...

NEEDD HELP! parameterizing a surface given by an implicit function (HYPERBOLOID?!) Homework Statement I need to parameterize the surface given by the following implicit equation: x2 + y2 + z2 + 2xy + 2xz - 2yz = 1 Homework Equations I tried using all sorts of subsititutions...

2 = xy^2/(x^2+y^2) is this what you're talking about? how do I isolate x?

how would you express this equation explicitly in x?

I think I'm getting there...tell me if this makes sense to you: if we let the paths be: x=y and y=x: then the equations reduce to f(x,y=x) = x/2 f(x=y,y) = y/2 taking the limits of these two equations x-->a gives a/2 y-->a gives a/2 a/2=a/2 = a then the limit is a along this...

so I took some values around zero of this function (N/D is @ zero)...and I see what you're saying..about the limit not exsisting: -0.05 0 -0.05 0 N/D 0 0.05 0 0.05 but if we let f(x,y) = a = or equal say, z ... then we can show that the limit...

how do I prove that with this paticular problem then?

y is decreasing towards zero from the positive side, and x is increasing towards zero from the negative side. for the limit to exist, we have to approach a value along all paths that lead to that value, correct?

So how does setting x(y) or y(x) help me in this equation? I'm assuming I don't have to prove the actual limit of the function do I? I'm assuming its going to be zero, just from using some polar equations, x=rcosθ and y=rsinθ , and letting the function approach r . I know that showing the limits...