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Vectors and Curvature

Find k(t) for y = 1/x.
P.S. The curvature of a curve is k = dT/ ds, where T is the unit tangent vector.
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And k(t) = T'(t)/ r'(t)

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Vectors and curvature are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.