91Ó°ÊÓ

\- Let \(f(x)=m x+b\) and \(\left(x_{0}, y_{0}\right)\) be a point not on the graph of \(f(x)\). Find the point on the graph of \(f(x)\) that is closest to \(\left(x_{0}, y_{0}\right)\).

Let \(R\) denote the region in the first quadrant bounded by the graphs of \(y=x^{n}\) and \(x=y^{n}\). (a) Find the area of \(R\). (b) Find the volume of the solid obtained by revolving \(R\) about the \(x\)-axis. (c) Find the volume of the solid obtained by revolving \(R\) about the \(y\)-axis.