Chapter 13.3, Problem 47E

Curvature of Plane Parametric Curves The curvature of a plane parametric curve $x=f(t),y=g(t)$ is given by

$\kappa =\frac{|\stackrel{.}{xy}-\stackrel{\dot{}}{y}\ddot{x}|}{{\left[{\stackrel{\dot{}}{x}}^2+{\stackrel{\dot{}}{y}}^2\right]}^{3/2}}$ where the dots indicate derivatives with respect to $t$ .

47. Find the curvature of the curve $x=t^2,y=t^3$ .