CHAPTER 1—Limits and Their Properties

CHAPTER 1—Limits and Their Properties

1.1—A Preview of Calculus1.2—Finding Limits Graphically and Numerically1.3—Evaluating Limits Analytically1.4—Continuity and One-Sided Limits1.5—Infinite Limits

1.1—A Preview of Calculus http://hmco.tdlc.com/public/calc7esample/calc7emain.htmlCh.11.1

What IS calculus, and how does it relate to pre-calculus?

What is the “tangent line problem”? What is the “area problem”?

Essential Questions

Mathematics of change (look at table on the bottom of the page)

What is Calculus?

Pre-Calculus

Limit Process Calculus

The Tangent Line Problem

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Ch.11.1The Tangent Line Problem

The Area Problem

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Ch.11.1The Area Problem

Practice Problems

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Ch.11.1Section Exercises

1,3,11

1.2—Finding Limits Graphically and Numericallyhttp://hmco.tdlc.com/public/calc7esample/calc7emain.html

What do we mean when we talk about the “limit” of a function?

How should you interpret the following?

Compare and contrast the numerical and graphical approaches for finding the limit of a function.

Under what circumstances would a limit fail to exist?

Essential Questions

An Introduction to Limits

http://hmco.tdlc.com/public/calc7esample/calc7emain.htmlCh.11.2

Limits that Fail to Exist

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Ch.11.2Limits that Fail to Exist

The Formal Definition of the Limit

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Ch.11.2The Formal Definition of a Limit

Practice Problems4,7-9,12,1623,35,3844-46

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Ch.11.2Section Exercises