Chapter 3

1.     Section 3.1

1.     Definitions

1.     limit of a function at a point, x_o (2 definitions)

2.     right and left hand limits of a function at a point, x_o

2.     Theorems

1.     Algebra of Limits Theorem for Functions (SAL)

2.     Squeeze Theorem for Functions

3.     Gordon Problems 2,6,9,10,13, 23,24,27,28,32

2.     Section 3.2

1.     Definitions

1.     f is continuous at x_o (2 definitions)

2.     f:A->B is continuous

3.     f has a jump discontinuity at x_o

4.     f has a removable discontinuity at x_o

2.     Theorems

1.     Algebra of Continuous Functions Theorem (DAL)

2.     Polynomials are everywhere continuous

3.     Rational Functions are continuous except at poles.

3.     Gordon Problems 1,4,6,7,8,9,10,13,16,18

3.     Section 3.3

1.     Definitions

1.     intermediate value of a function f:A->B

2.     f has the intermediate value property on a set A

3.     extreme value of a function f:A->B

4.     f is locally bounded

5.     the set E is compact

2.     Theorems

1.     Intermediate Value Theorem

2.     Extreme Value Theorem

3.     If the domain of a continuous function is compact, so is the range

4.     If the domain of a continuous function is an interval, so is the range

5.     If f is monotone, f has only jump discontinuities

6.     If f is monotone, f has at most countably many discontinuities

7.     A monotone function with the intermediate value property is continuous.

8.     A continuous strictly monotone function has a continuous strictly monotone inverse.

3.     Gordon Problems 1,5,6,7,11,13,16,18,27,34,39