Information about Exam III for Math 2423-001H

Mathematics 2423-001H - Honors Calculus II - Spring 2007

Information about Exam III

Exam III will be in the usual classroom on Thursday, April 26, 2007. It will cover sections 7.6-7.7 and 8.1-8.4.

Calculators or other mechanical assistance are not needed and are not to be used. Blank paper will be provided, so all you will need is something to write with.

Many of the exam problems will be from the homework, or very similar to homework problems. One problem will be repeated from Exam II. As usual, the exam has more than 50 points possible. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others.

The following topics are very like to appear, although the exam is not necessarily limited to these topics:

  1. Hyperbolic trigonometric functions.
  2. Integrals involving powers of trigonometric functions.
  3. Integration by parts.
  4. Integration of rational functions; the method of partial fractions.
  5. Inverse substitutions; trigonometric substitutions for common expressions such as a² - u², u² - a², a² + u². Expressing the result in terms of the original variable.
  6. l'Hôpital's rule. Standard indeterminate forms, including variable expressions with variable exponents (i. e. the indeterminate forms \infty⁰ and 1^\infty).

One must know the derivative and integral formulas involving the six trig functions, including formulas 1-16 in the table on page 542. One must know the identities involving squares of trig functions, including the expressions for sin²(x) and cos²(x) in terms of cos(2x). It is not necessary to know the identities used to integrate the expressions sin(mx)sin(nx), sin(mx)cos(nx), or cos(mx)cos(nx). One must know integration by parts very well. There will not be problems of integration using tables. It is not necessary to memorize identities involving the hyperbolic trig functions. Of course, one should be familiar with their graphs, and the more basic derivative and integral formulas for them.

Exams from previous Honors Calculus classes can be found on their course pages (links to them appear on the course pages page). Some were 50-minute classes, but most were 75-minute classes. Of course, these were different courses, so the exams may be quite a bit different.

1.	Hyperbolic trigonometric functions.
2.	Integrals involving powers of trigonometric functions.
3.	Integration by parts.
4.	Integration of rational functions; the method of partial fractions.
5.	Inverse substitutions; trigonometric substitutions for common expressions such as a² - u², u² - a², a² + u². Expressing the result in terms of the original variable.
6.	l'Hôpital's rule. Standard indeterminate forms, including variable expressions with variable exponents (i. e. the indeterminate forms \infty⁰ and 1^\infty).