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Appendix B Definitions

1 Introduction to the course

Definition 1.1 Function
Definition 1.10 Sets and set membership
Definition 1.11 Subsets
Definition 1.12 Set-builder notation

2 Limits: informal definition

Definition 2.1 Graph of function
Definition 2.5 Function defined on set
Definition 2.6 Limit (informal)

3 Limits: algebraic technique and sandwich theorem

Definition 3.9 Absolute value

4 Limits: formal definition

Definition 4.1 Limit (formal)

5 One-sided limits

Definition 5.1 One-sided limits
Definition 5.5 Limit at endpoints of domain

6 Continuity: definition

Definition 6.1 Interior points and endpoints
Definition 6.2 Continuity

8 Limits at infinity

Definition 8.1 Limits at infinity
Definition 8.5 Horizontal asymptote

9 Infinite limits

Definition 9.1 Infinite limits (informal)
Definition 9.4 Vertical asymptote

10 Derivative: at a point

Definition 10.1 Derivative at a point
Definition 10.5 Difference quotient
Definition 10.6 Derivative interpretations

11 Derivative: function

Definition 11.1 Derivative function
Definition 11.8 Leibniz notation

12 Derivative: rules

Definition 12.9 Higher order derivatives

13 Derivative as rate of change

Definition 13.3
Definition 13.5 Marginal cost, revenue, profit

14 Derivative: trig functions

Definition 14.3 Trigonometric functions

19 Linearization

Definition 19.1 Linearization of a function

20 Extreme value theorem

Definition 20.6 Extreme values
Definition 20.12 Critical point

22 Monotonicity and first derivative test

Definition 22.1 Increasing, decreasing, monotonic

23 Concavity and inflection points

Definition 23.3 Concavity and inflection points