Chapter 5.1, Problem 56E

In the following exercises, the functions $f_n$are given, where $n\ge 1$ is a natural number.

a. Find the volume of the solids S,, under the surfaces z = f(x. y) and above the region R.

b. Deteimine the limit of the volumes of the solids S as n increases without bound. 55. $f\left(x,y\right)=x^n+y^{n}xy,\left(x,y\right)\in R=\left[0,1\right]\times \left[0,1\right]$