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Help hlp with another math problem plz

a dallop a d-
aisy

Avatar: Webcam Girl

Level 6 Camwhore

“Training Broad”

hlp from my diff. geo. book i dun get it:

Let κ(s) (>0) and τ(s) be continuous functions of a real variable s, defined in an interval I: 0≤s≤a. The formulae of Frenet

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are three systems of ordinary linear differential equaations of the unit vectors t, the unit tangent vector, p, the principle normal unit vector, and b, the binormal unit vector, of the moving trihedron,

(20.1) Log in to see images!

For the sake of simplicity, we set

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Therefore we have, written in vector form, differential equations of the type

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We write these equations again in scalar form, omitting the index i by which the different components of the vectors Log in to see images! are denoted, that is, we write (20.1) in the form

(20.1’ ) Log in to see images!

In (20.1’ ) the elements of the coefficient matrix

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are continuous functions in the closed interval I: 0≤s≤a and consequently bounded in I,

(20.2) Log in to see images!

a dallop a d-
aisy

Avatar: Webcam Girl

Level 6 Camwhore

“Training Broad”

We have to prove that there exists a solution of (20.1) or of (20.1’ ) satisfying given initial conditions, say

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where we have to bumume that Log in to see images!,

(20.3) Log in to see images!

must hold. Replacing the functions Log in to see images! we obtain three first approximate functions

(20.4) Log in to see images!

If we insert these first approximate functions Log in to see images!th approximate functions

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We have to prove that when n increases arbitrarily Log in to see images! we obtain from (20.2) and (20.4)

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similarly, Log in to see images!

and in general

(20.6) Log in to see images!

naw, its this equation (20.6) (and the one above it) that confuses me; im sure why that factorial n! is there, somehow u are able to divide by n but im not sure why

Skyreal

Avatar: Boobs
8

Level 24 Camwhore

“The Lady is a Tramp”

You mean like this?

n! = 1×2 x 3 x … x (n-2) x (n-1) x n

n!/n = 1×2 x 3 x … x (n-2) x (n-1) = (n-1)!

EDIT: Hold on, I took a closer look and I know what you mean now. Let me look a little longer. Log in to see images!

EDIT: I’m a little confused, but it seems to me that when you integrate Vk^(n-1) you end up with n in the denominator, and the rest is supposed to work out. I didn’t actually do the work though.

Skyreal edited this message on 03/08/2008 11:07AM
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