MTH 435 Fall 05 -- Tips for Exam 2

Exam 2 is scheduled for Friday, November 18, 3-5, in Tyler 106.

Exam 2 covers classes 10-18 and homework assignments 5-8. You are expected to know and be able to state all definitions, propositions, and theorems given in class and in homework assignments as well as their proofs. You should know all of the important examples studied in class. You are expected to know solutions to all homework problems. Some problems on the exam may be very similar to homework problems.

Expect problems of the same type as on Exam 1. A few sample candidates:

-- Problem. (a) State the definition of a Cauchy sequence. (b) Prove that every convergent sequence is Cauchy (or the converse).
-- Problem. (a) State the Squeeze Theorem for sequences. (b) Prove the theorem.
-- Problem. Prove that the limit of the product of two convergent sequences is the product of their limits.
-- Problem. (a) Define the right limit of a function at a point. (b) State and prove Heine's characterization of the right limit. (H7 #4).
-- Problem. Something like # 3 H7.
-- Problem. Something like # 3 H8. (See the correction on the main page!).
-- Problem. (a) State the Boundedness Theorem. (b) Prove the theorem.
-- Problem. Give an example of a function which has no limit at any point. Prove your claim.

These are only examples of the types of problems you should expect (they may or may not appear). I hope you all get As!