Chapter 12.5, Problem 75E

To determine

To prove: The curvature of function $x=f\left(t\right)$ and $y=g\left(t\right)$ is $k=\frac{\left|f^{\prime }\left(t\right)\cdot g^{″}\left(t\right)-g^{\prime }\left(t\right)\cdot f^{″}\left(t\right)\right|}{{\left\{{\left[f^{\prime }\left(t\right)\right]}^2+{\left[g^{\prime }\left(t\right)\right]}^2\right\}}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$.