find the curvature of r(t) = at the point (5, 1, 1).
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find the curvature k of the curve at the point p. r(t) = et cos(t)i + et sin(t)j + etk, p(1, 0, 1).
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5. Do the following tasks using Mathematica
For a Parametric curve χ = χ (t) , y = y(t) the curvature at a point p is:
(a) Parametric equations of the cycloid are:
(b) Show that the curvature at top of any one of cycloid's arches is 1/4.
Hint: At top of any one of it's arches y is maximum
(c) Parametric equations of a circle of radius r are:
Show that the curvature of each point of a circle of radius r is K = 1/r
Find the radius it Curvature of the Curvexy=1 at the point (1,1)