Math 1571H Honors Calculus Fall Semester 2001

Assignment 5 - Due Thursday 10/11/2001

Read: Simmons Sections 2.5, 2.6, 3.1, 3.2
Section 2.6 is about some abstract theorems which are fundamental to the development of the theory. I will indicate proofs to you in class, but you will not be tested on proofs in the exams. What you may be tested on is applications of the results, similar to what you have to do in the exercises at the end of the sections.
The sections in Chapter 3 are about the rules for differentiating basic kinds of functions, and there are various formulas such as the product rule, the quotient rule, the chain rule etc. You need to remember these and also get a lot of practice using them. You will not be tested on the proofs of the formulas. It may be that you already have a lot of practice applying the quotient rule etc, because you have done it before. If you do not already have practice with these rules for differentiation, then you should work more problems from the end of the sections than what I specify here. There are many problems available, e.g. 1 - 34 at the end of section 3.2. Make sure you can do these rapidly and accurately. It is like learning a language, and the best thing is to practice again and again using the expressions you are supposed to grasp.

Exercises:
Sec 2.5: 4, 5, 6, 8*, 9, 15, 16*, 18c, 18d*, 20a*, 20b*, 20c, 20d, 20e*, 20f, 20g
Sec 2.6: 2*, 5, 7, 8, 11, 12*, 14*, 34*, 35, 39
Sec 3.1: 4, 6, 14* 18, 22
Sec 3.2: 6, 12, 14, 17, 42*
Extra Question: Match the graph of each function in (a) - (f) with the graph of its derivative in (i) - (vi). *Hand in the result for part (d) with an explanation.

There are 12 graphs which should appear here, and are not present in this version.