In general, calculating \(\vN\) as a function of the parameter \(t\) ends up being very difficult because there are multiple compositions of functions involved which means there is a nesting of chain rules involved in the definition. In this activity, we will examine how to go through the direct calculation of \(\vN\) for a curve parameterized by \(\vr(t) =\langle t,t^2,t^3\rangle \text{.}\)
In the previous part, you likely decided that trying to simplify your formulas for \(\frac{d\vT}{dt}\) and \(\vecmag{\frac{d\vT}{dt}}\) was more complicated than you had space for on your paper. Instead of doing more intricate algebraic computations, describe how you would calculate \(\vN\) if you had nice formulas for \(\frac{d\vT}{dt}\) and \(\vecmag{\frac{d\vT}{dt}}\text{.}\)
