section	note to yourself of date due	problems
4.1 and 4.2 Handouts		Basic Topology and Continuous Functions   informal notes by Girardi Limit of a Function   by Bilodeau and Thie Limits and Continuity of Functions   by Krantz
4.1 Limit of a Function		Pick 4 from:     1f, 6, 8f, 10, 14a, 17b, 19.
4.2 Continuous Functions		Pick 2 from:     2, 17, 19, 20. Pick 2 from:     24, 30. Hint on 17: see proof of Cor. 4.2.14. Hint on 30: the following Lemma might be helpful. Lemma. Let A ⊆ R and p ∈ R. Then p is in the closure of A if and only if there exists a sequence {pn } from A such that lim n → ∞ pn = p. Proof of Lemma. You should be able to show this by piecing together Def 3.1.10, Thm 2.4.7, and Exercise 3.1.5.
4.3 Uniform Continuity		Pick 2 from:     2b/3b/4b, 10, 11, 14.
4.4 Montone Fns & Discont.		Pick 2 from:    8, 9, 19, 20.
Chapter 4 Miscellaneous Exercises		Pick 1 from:    2, 3.
5.1 The Derivative		Pick 2 from:    13, 14, 16. Notes on the Chain Rule via Caratheodory's Differentiation Thm.
5.2 Mean Value Theorem (MVT)		13 (race track principle, used often), 14. Pick 1 from:    6, 9. Pick 1 from:    18, 19 Also, read (and be responsible for) the parts of this section not covered specifically in class (pages 182 - 187). These are further applications of the MVT. Notes on Cauchy's MVT.
5.3 & 5.4		§ 5.3 (L'Hospital's Rule) and § 5.4 (Newton's Method) are further applications of the MVT. Read these 2 sections for your general knowledge.
Chapter 5 Miscellaneous Exercises		Pick 2 from:    1, 2, 5 sol'n, 6.
Chapter 5 Convex Functions		Class Handout # 1 and Class Handout # 2. Notice that convex functions are covered in the textbook in Ch. 5 Misc. Exercises # 3. The sol'n to these problems can be found in the class handout: 3a: Proposition 3.2 part 1 3b: Proposition 3.2 parts 2 and 3 3c: Theorem 4.1 part 4.1.2.