Information about the Final Exam for Math 1823-010

Mathematics 1823-010 - Calculus I - Spring 2001

Information about the Final Exam

The Final Exam will be in the usual classroom on Monday, May 7, 2001, from 8:00 a. m. to 10:15 a. m.

It will be worth 77 points (2 extra points possible). There will be nine questions in multiple-choice format, worth a total of 20 points. Some of the multiple-choice questions will refer to values of functions and their derivatives given in a table. About 24 points of the exam will be material from sections 4.7 and 4.10, the sections that were not covered in one of the in-class exams.

Only a basic, non-graphing calculator may be used. Actually, there is little if any need to use a calculator.

We hope to grade the exams during the day Monday, and post final course grades on the course website by sometime in the evening. Solutions to the Final Exam will be posted the afternoon of Wednesday, May 9. You may pick up your graded exam from me any time during the next year; after one year it will become recycled paper.

The following will definitely be covered:

  1. Knowing and understanding statements of major theorems (the Fundamental Theorem of Algebra, the Intermediate Value Theorem, the Extreme Value Theorem, Rolle's Theorem, the Mean Value Theorem).
  2. Sections 3.6, 3.9, and 4.7.
  3. The epsilon-delta definition of limits, and its application to an easy limit such as a limit of a linear function, or of a power or root function as x --> 0.
  4. Sketching the graph of the derivative of a function, given the graph of the function. Sketching the graph of an antiderivative of a function, given the graph of the function.
  5. Finding all antiderivatives f(x), given f '(x) or f ''(x), and possibly values of f(x) at a point.

The following sections will not be directly covered. That is, there will not be any questions taken directly from the problems studied in these sections: 1.1-1.3, 2.1, 2.6, 3.4, and 4.9.

The following topics will not be directly covered: the limit laws, differentials, calculation of secant lines, calculation of limits (although as indicated above, there will be an epsilon-delta proof of some obvious limit), calculation of derivatives using the limit definition, calculation of velocity or acceleration from the position function, approximation using polynomials of degree 2 or higher.

It will be necessary to know the derivatives of all six trigonometric functions from memory, and be able to reproduce important definitions in precise mathematical language.

1.	Knowing and understanding statements of major theorems (the Fundamental Theorem of Algebra, the Intermediate Value Theorem, the Extreme Value Theorem, Rolle's Theorem, the Mean Value Theorem).
2.	Sections 3.6, 3.9, and 4.7.
3.	The epsilon-delta definition of limits, and its application to an easy limit such as a limit of a linear function, or of a power or root function as x --> 0.
4.	Sketching the graph of the derivative of a function, given the graph of the function. Sketching the graph of an antiderivative of a function, given the graph of the function.
5.	Finding all antiderivatives f(x), given f '(x) or f ''(x), and possibly values of f(x) at a point.