r(t) = < e^t * cost, e^t*sint, 5>

Find the curvature at the point (x, y, z) = (-e^π, 0, 5)

explain briefly how you come up with answer and also express answer as a decimal.

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- Apr 16th 2012, 08:11 PMkayla12345Curvature
r(t) = < e^t * cost, e^t*sint, 5>

Find the curvature at the point (x, y, z) = (-e^π, 0, 5)

explain briefly how you come up with answer and also express answer as a decimal. - Apr 17th 2012, 04:24 AMMathoManRe: Curvature
If a point belongs to a curve then exists a parameter value such that

. In case of a given point

Wikipedia says that for a space curve its curvature is given by

http://upload.wikimedia.org/wikipedi...077bf036b1.png.

All derivatives are with respect to variable t. Here is a function in variable , Find the expression for and evaluate it for . - Apr 17th 2012, 04:55 AMtom@ballooncalculusRe: Curvature
Also, notice that as z is constant you are really looking at,

http://www.ballooncalculus.org/draw/graph/curvature.png

... so you only need the 2-D version (Curvature - Wikipedia, the free encyclopedia).

Just in case a picture helps differentiate...

http://www.ballooncalculus.org/draw/diffProd/eight.png

... where (key in spoiler) ...

__Spoiler__:

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Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

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