Thread: Curvature

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.

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
.

All derivatives are with respect to variable t. Here is a function in variable , Find the expression for and evaluate it for .

Also, notice that as z is constant you are really looking at,



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

Just in case a picture helps differentiate...



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

Spoiler:

... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to t. And,

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