Information about Exam III for Math 2423-001H

Mathematics 2423-001H - Honors Calculus II - Spring 2005

Information about Exam III

Exam III will be in the usual classroom on Thursday, April 28, 2005.

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

The exam might be on the long side, so avoid spending a lot of time on any individual problem unless you have completed all the other problems that you definitely know how to do. That is, grab easy points first. The exam will be the usual mix, but will have a higher density of homework problems than the previous exams.

The main topics are the exponential and logarithm functions. The following will definitely be covered (of course, the exam is not limited to these topics):

  1. Inverse trig functions, focus on the inverse sine and inverse tangent functions. Know how to use triangles to simplify expressions of the form trig(trig^-1(*)).
  2. Hyperbolic trig functions. Know the definitions, graphs, basic identities, and basic calculus. It is enough to focus on sinh(x), cosh(x), and tanh(x).
  3. L'Hôpital's rule and how to apply it to all the standard indeterminate forms.
  4. Techniques of integration, including integration by parts, integrands that are various combinations of trig functions, and ``inverse'' substitutions (i. e. trig substitutions such as x = a sin(u)).
  5. Decomposition of rational functions into partial fractions. Be able to write the form of the partial fraction decomposition of a rational function.
  6. Integration using tables.
You should know the standard trig identities including the ones to express sin²(x) and cos²(x) in terms of cos(2x). You do not need to know the integrals of sec(x) or csc(x), or the identities for simplifying expressions of the form sin(A)cos(B), sin(A)sin(B), or cos(A)cos(B).

The following do not appear on Exam III: inverse hyperbolic trig functions, reduction formulas, numerical approximation of integrals (Simpson's rule).

1.	Inverse trig functions, focus on the inverse sine and inverse tangent functions. Know how to use triangles to simplify expressions of the form trig(trig^-1(*)).
2.	Hyperbolic trig functions. Know the definitions, graphs, basic identities, and basic calculus. It is enough to focus on sinh(x), cosh(x), and tanh(x).
3.	L'Hôpital's rule and how to apply it to all the standard indeterminate forms.
4.	Techniques of integration, including integration by parts, integrands that are various combinations of trig functions, and ``inverse'' substitutions (i. e. trig substitutions such as x = a sin(u)).
5.	Decomposition of rational functions into partial fractions. Be able to write the form of the partial fraction decomposition of a rational function.
6.	Integration using tables.