Math 141, Spring 2016, Assignment 5

I was at the mathematical school, where the master taught his pupils after a method scarce imaginable to us in Europe. The proposition and demonstration were fairly written on a thin wafer, with ink composed of a cephalic tincture. This the student was to swallow upon a fasting stomach, and for three days following eat nothing but bread and water. As the wafer digested the tincture mounted to the brain, bearing the proposition along with it.

- Jonathan Swift, Gulliver's Travels

Carefully state the following theorems (you do not need to prove them):

1. Direct comparison test for improper integrals.
2. Limit comparison test for improper integrals.

Solve the following problems:

1. Section 6.8, problems 2, 3, 4, 5, 6, 7, 9, 13, 15, 17, 19, 21, 23, 35, 37, 39, and 41.

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