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

Information about Exam III

Exam III will be in the usual classroom on Thursday, December 2, 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 on the homework assignments. It will be similar to Exams I and II in length.

The exam covers sections 4.1-4.5 and 4.7. The following topics will definitely be covered (but the exam is not limited to these topics):
  1. the Mean Value Theorem, precise statement, applications
  2. the Extreme Value Theorem, precise statement
  3. local extreme values and absolute extreme values of functions (note that unlike the textbook, our definitions allow a local extreme to occur at an endpoint of the domain)
  4. determining graphs of functions and their noteworthy features, using f', f'', and other ideas
  5. optimization problems

You should know the interval notations (a,b), [a,b), (a,b], and [a,b]. Now and forever you are expected to know the derivatives of the six trigonometric functions.

The following will not appear on the exam: I(x) (the inverse function of the exponential), sequences and their convergence behavior, the reasoning used to establish the Extreme Value Theorem, the reasoning used to establish the Mean Value Theorem using the Extreme Value Theorem, inverse trigonometric functions, Rolle's theorem (other than as a case of the MVT), verifying limits as x ---> \infty using the precise definition of limit, slant asymptotes