Use the result of Exercise 77 to find the curvature K of the curve represented by the parametric equations x(t) = t³ and y(t) = 1/2t². Use a graphing utility to graph K and determine any horizontal asymptotes. Interpret the asymptotes in the context of the problem.

Data from in Exercise 77

For a smooth curve given by the parametric equations x = ƒ(t) and y = g(t), prove that the curvature is given by

Transcribed Image Text:

K = [ƒ'(t)g"(t) — g'(t)ƒ"(t)[ {[f'(t)]²+ [g'(t)]²}³/2.