?In the following exercises, the functions \(f_{n}\) are given, where \(n \geq 1\) is a

Chapter 5, Problem 56

(choose chapter or problem)

In the following exercises, the functions \(f_{n}\) are given, where \(n \geq 1\) is a natural number.

a. Find the volume of the solids \(S_{n}\) under the surfaces \(z=f_{n}(x, y)\) and above the region R.

b. Determine the limit of the volumes of the solids \(S_{n}\) as n increases without bound.

\(f(x, y)=\frac{1}{x^{n}}+\frac{1}{y^{n}},(x, y) \in R=[1,2] \times[1,2]\)

Text Transcription:

f_n

n geq 1

S_n

z = f_n (x, y)

f(x, y) = 1/x^n + 1/y^n, (x, y) in R = [1,2] times [1,2]