Module 4. Limits and Continuity
  1. Limits

    Objectives:
    After working through the Readings, Web Materials and the Homework, the student should be able to
    • understand graphically the definition of limits;
    • find graphically d when given e;
    • understand the relationship between a limit and the right-hand and left-hand limits;
    • apply the squeeze theorem.

    Readings:
    • Section 2.3 and Appendix D of Stewart.

    Web Materials:

    Homework Problems: (due September 25)
    • Stewart p.118: 20, 21, 31, 32
      Stewart p.A39: 1, 2, 3, 4, 5, 6


  2. Continuty

    Objectives:
    After working through the Readings, Web Materials and the Homework, the student should be able to
    • understand the definition of continuity;
    • be able to derive theorems about combining continuous functions and to apply these theorems;
    • understand graphically the concept of a continuous function;
    • understand and apply the Intermediate Value Theorem;
    • understand and apply the Bisection Method to approximate roots of equations and be able to calculate the error in this approximation.

    Readings:
    • Section 2.4 of Stewart

    Web Materials:

    Homework Problems: (due September 28)
    • Stewart p.129: 3, 11, 12, 14, 27, 28, 31, 33, 34, 39(Use bisection method).


  3. Infinite Limits

    Objectives:
    After working through the Readings, Web Materials and the Homework, the student should be able to
    • find vertical and horizontal asymptotes of functions.

    Readings:
    • Section 2.5 of Stewart.

    Web Materials:

    Homework Problems: (due September 30)
    • Stewart p.140: 3, 15, 17, 19, 20, 21, 22, 23, 33, 40, 41


  4. Using the Definition of Derivative

    Objectives:
    After working through the Readings, Web Materials and the Homework, the student should be able to
    • use the properties of limits and techniques of evaluating limits to calculate the derivative at a point.

    Readings:
    • Section 2.7 of Stewart.

    Web Materials:

    Homework Problems: (due October 2)
    • Stewart p.156: 8, 9, 15, 24