Unit 1 Limits and Continuity

You’ll start to explore how limits will allow you to solve problems involving change and to better understand mathematical reasoning about functions.

Throughout the course we will identify and represent mathematical information four ways: (1) graphically, (2) numerically, (3) analytically, and (4) verbally.

Your mastery will be assessed not only by the value or expression you determine, but how you express your reasoning using correct language and notation.

How limits help us to handle change at an instant
Definition and properties of limits in various representations
Definitions of continuity (1.4) of a function at a point and over a domain
Asymptotes and limits at infinity (1.5)
Reasoning using the Squeeze theorem (section 1.3 p69) and the Intermediate Value Theorem (1.4 p81)

1.1	Introducing Calculus: Can Change Occur at an Instant?
1.2	Defining Limits and Using Limit Notation
1.3	Estimating Limit Values from Graphs
1.4	Estimating Limit Values from Tables
1.5	Determining Limits Using Algebraic Properties of Limits
1.6	Determining Limits Using Algebraic Manipulation
1.7	Selecting Procedures for Determining Limits
1.8	Determining Limits Using the Squeeze Theorem
1.9	Connecting Multiple Representations of Limits
1.10	Exploring Types of Discontinuities
1.11	Defining Continuity at a Point
1.12	Confirming Continuity over an Interval
1.13	Removing Discontinuities
1.14	Connecting Infinite Limits and Vertical Asymptotes
1.15	Connecting Limits at Infinity and Horizontal Asymptotes
1.16	Working with the Intermediate Value Theorem (IVT)

Unit 1 Limits and Continuity

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