Mathematica

This entire problem must be done using Mathematica.

You will be using the function f(x) = 1/x

1.Use the RevolutionPlot3D command to graph the solid obtained by rotating f(x) about the x-axis. Let the x values go from x = 1 to x = 5. Get rid of the box!

2.Describe the shape of a typical cross-sectional slice of the solid. And then write down the formula of the area of that cross section.

3.Use an integral to express the total volume of this solid between x = 1 and infinity. You do not have to attempt to solve it yet, but you need to explain why the integral represents the volume described.

4.Without doing the integral in Mathematica or by hand, discuss how you know that this integral will converge.

5.Use Mathematica to solve this integral. This is improper! Describe what commands you are using and why they are necessary!

6.Discuss instead how you could compare the integral you have to a simpler integral that we know diverges. Use the comparison theorem to show that your surface area integral diverges.

7.Restate your results for the volume and surface area. Discuss (this is very general, what do you think about it?) the apparent paradox in having these answers together for a solid.