Unit One: Limits and Continuity

Before you tackle this unit you should take the time to review your precalculus. Make sure your algebra and trigonometry skills are up to par, or else you may find yourself confused before you actually get to any calculus.

Limits are essential to differentiation. In this section, we develop the concept of the limit and continuity. The limit can be looked very formally, or very informally. We'll try to take some sort of middle ground.

Objectives

Review precalculus concepts
Limits
- Get an intutive feel for limits
- Read and understand the formal definition of the limit
- Learn methods for evaluating limits
- Look at the special trig limits
Continuity
- Relate continuity to limits
- Get an intuitive feel for continuity
- Read and understand the formal definition of continuity

Suggested Procedure

Read
- Simmons, first edtiton
  - Chapter 1
  - Section 2.5
  - Appendix C, sections 1-3 (optional)
- Simmons, second edition
  - Chapter 1
  - Section 2.5 and 2.6 (just the part about continuous functions)
  - Appendix A, sections 1-3
- World Web Math
- Do Problems in Simmons
  - 1.6 : #5
  - 1.7 : #7, 9, 11, 13
  - 1.8 : #1
  - 2.5 : # 3, 7, 11, 17, 18, 19
- Take the Practice Unit Test, Xdvi or PDF.
- Ask your instructor for a unit test.
Independent Study Page | Calculus Page World Web Math Categories Page

watko@mit.edu
Last modified July 30, 1998