Exam III will be in the usual classroom on Wednesday, November 16, 2011. It will cover sections 7.3* and 7.4*, 7.6-7.8, and 8.1-8.2, but only the material that we discussed in class. The current draft has 53 points.

Some of the questions will be basic or straightforward, others will be more difficult ones that I do not expect many students to be able to answer. Grades in the 90% range are certainly not required to be doing A work.

The exam is on the long side, but do not make it longer than it is. Many of the questions have rather short answers if you simply do what they ask for, so be sure you understand each question and give whatever answers are requested, no more and no less. But be sure complete all the questions that you definitely know how to do, before spending time on the ones that may be more difficult.

Calculators are not needed, although you may, if you really want to, use a non-graphics simple arithmetic calculator without even trig functions, but no mechanical or electronic device more sophisticated that this (including iPods, earpieces, etc.). I will provide blank paper on which you can write your answers. Please put your name on your exam paper itself and all pages of your solutions, and hand them all in together, although without any pages of scratch work that is not to be graded.

Definitions of important concepts are (of course) perfectly reasonable questions, and although you do not need to know them word-for-word, you should be able to write down a coherent and accurate definition of any major concept or term.

Obviously not every single item can be covered in depth in a 50-minute exam. The following topics are very likely to appear, although the exam is not limited to them:

1. Exponential function. There are not a lot of specific questions about it, but it is involved in a lot of the problems.
2. Logarithms and exponentials to other bases. You can know the differentiation formulas, but can also get by just knowing that log_a(x) = ln(x)/ln(a) and a^x=e^{x ln(a)}.
3. Inverse trig functions, their definitions, general properties, integration and differentiation formulas involving them. They are rather important.
4. Hyperbolic trig functions. There is some coverage, but not a lot.
5. l'Hôpital's rule. Quite a bit of coverage.
6. Integration by parts. A fundamental technique.
7. Trig integrals. Not a lot of coverage, but practice some integrals.

The following do not appear on this exam: expression for the error of linear approximation as an integral, Fourier series, inverse hyperbolic trig functions, proof of l'Hôpital's rule, deeper properties of the graph of the exponential function, integration of the products sin(mx) sin(nx), sin(mx) cos(nx), and cos(mx) cos(nx).

Previous exams I have written for regular and honors calculus classes are available at their course pages on my website. Links to those pages are listed at course pages page). Some of those classes met twice a week, so the exams were geared to a 75-minute time period. Taking one of those exams and checking your solutions might be good practice, especially if you tend to get test anxiety, but be aware that those were different courses with different emphases. When I sit down to write an exam, I never look at old exams I have written. I start with a blank page and think about what we did in the present course, and try to find problems that will give some measure of what you have learned.