Information about Exam I for Math 1823-001H

Mathematics 1823-001H - Honors Calculus I - Fall 2004

Information about Exam I

Exam I will be in the usual classroom on Thursday, September 23, 2004.

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 will be based on our classroom discussions and (perhaps to a lesser extent) on the homework assignments. It will have approximately 10 problems, and it is not expected that you will be able to do all them. Just relax, do your best, and move on to your next task in life.

The following topics will definitely be covered (of course, the exam is not limited to these topics):

  1. manipulation of graphs of functions using the expressions f(kx), kf(x), f(x) + k, and f(x - k)
  2. operations on functions, even and odd functions
  3. slopes of secant lines and slopes of tangent lines
  4. limits: intutitive meaning; calculations; epsilon-delta definition including cases of L = infinity or - infinity, a = infinity or - infinity, and/or one-sided limits; use of the epsilon-delta definition
  5. continuity, the Intermediate Value Theorem, statement and applications
  6. using the fact that f( a + h ) = f(a) + mh + epsilon(h) with lim_{h\to 0} epsilon(h)/h if and only if m is the rate of change of f at the x-value a.

There will not be difficult or complicated applications of the epsilon-delta definition of limit, such as proving that the limit of a product is the product of the limits.

You may take as known the fact that lim_{h\to 0} sin(h)/h = 1.

The format of the exam will be similar to those of the exams that I wrote for Honors Calculus III and IV, which can be found on their course pages (links to them appear on the course pages page).

1.	manipulation of graphs of functions using the expressions f(kx), kf(x), f(x) + k, and f(x - k)
2.	operations on functions, even and odd functions
3.	slopes of secant lines and slopes of tangent lines
4.	limits: intutitive meaning; calculations; epsilon-delta definition including cases of L = infinity or - infinity, a = infinity or - infinity, and/or one-sided limits; use of the epsilon-delta definition
5.	continuity, the Intermediate Value Theorem, statement and applications
6.	using the fact that f( a + h ) = f(a) + mh + epsilon(h) with lim_{h\to 0} epsilon(h)/h if and only if m is the rate of change of f at the x-value a.