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#1 2006-05-14 01:38:14

renjer
Member
Registered: 2006-04-29
Posts: 51

Lagrange

Use Lagrange multipliers to find the minimum distance from the point (5,5,4) to the paraboloid z=4-x^2-y^2.

I know a lot about Lagrange multipliers, they're quite easy, but the problem is, how do you find the distance from a point in space to a surface?

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#2 2006-05-14 02:20:25

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,226

Re: Lagrange

I don't know about Lagrange multipliers and read about it here.

If your problem requires finding the distance between a point and a surface, the distance required must be the shortest distance to the point from normal to the surface!


Character is who you are when no one is looking.

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#3 2006-05-15 00:41:20

renjer
Member
Registered: 2006-04-29
Posts: 51

Re: Lagrange

Then how can I relate that to Lagrange multipliers? I know there is supposed to be 2 equations f(x,y,z) and g(x,y,z) but now I don't know which two equations can I use.

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#4 2006-05-15 02:37:32

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: Lagrange

you can set up a distance function,
maximize it or its square under the constraint z=4-x^2-y^2.


X'(y-Xβ)=0

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