Math Homework #1

This homework assignment is due Wednesday, October 5^th by 4 p.m., either to me in my office or else in our Homework Box. You may speak to your classmates and others (and me J) about these problems, but your write-up should be your own. Show your work!

Consider the region in the first quadrant bounded by y=4-x² and y=-2x+4. Revolve this region about the y-axis. Compute its volume twice, once integrating with respect to x and once integrating with respect to y.

Do the following problems from Schaum, pp. 287-288:

15, 18, 20, 23, 24

Consider the region in the first quadrant bounded by the x-axis, the curve y=ln(x), and the vertical line x=e². Revolve this region about the y-axis. Compute the resulting volume.

There are infinitely many hotels, and they are numbered as … -3, -2, -1, 0, 1, 2, 3, … . Each of these hotels has infinitely many rooms, which are also numbered by … -3, -2, -1, 0, 1, 2, 3, … . There are infinitely many guests who need rooms; they are numbered 1, 2, 3, … . Describe a scheme that will assign each guest to her/his own room, in such a way that every room is filled.