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![SOLVED:For a smooth curve given by the parametric equations x=f(t) and y=g(t), prove that the curvature is given by K=(|f^'(t) g^''(t)-g^'(t) f^''(t)|)/({[f^'(t)]^2+[g^'(t)]^2}^3 / 2)](https://cdn.numerade.com/previews/3354e388-91ba-4307-ae73-6bb8fa6fe7b7_large.jpg "SOLVED:For a smooth curve given by the parametric equations x=f(t) and y=g(t), prove that the curvature is given by K=(|f^'(t) g^''(t)-g^'(t) f^''(t)|)/({[f^'(t)]^2+[g^'(t)]^2}^3 / 2)")