MATH 150 - CALCULUS WITH ANALYTIC GEOMETRY I

• NOTES FOR CHAPTERS 0, 1, AND 2

(NOTATION GUIDE; REVIEW; LIMITS AND CONTINUITY)

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The notes through Section 3.6 are typed. The rest is handwritten.

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• CHAPTERS 1 AND 2 REVIEW OUTLINE

Chapters 1 and 2 Review Outline (last revised 7/27/09)

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• CHAPTER 0: FRONT MATTER / NOTATION GUIDE, AND

• CHAPTER 1: REVIEW

• CORRECTIONS to Page 1.10: Example 7 deals with the square root function, not the squaring function. Also, -9 (instead of 9) is not in the domain of f.

BIG FILE: Chapters 0 and 1 (pdf) (last revised 7/12/12)

SMALLER FILES (if you can’t get the big files):

Chapter 0 (pdf): Front Matter / Notation Guide (last revised 7/12/12)

Topic 1 (pdf): Functions (typed; last revised 7/12/12)

Topic 2 (pdf): Trigonometry I (typed; last revised 7/12/12)

Topic 3 (pdf): Trigonometry II (typed; last revised 7/12/12)

WEB SITES:

• My Precalculus site: Math 141. Algebra: Preliminaries, Chapter 1, and Section 2.7 on Nonlinear Inequalities. Trig: Chapters 4 and 5.

Precalculus site:

• Trig site with Java applets to play with!:

• Trig site: Look under "Trigonometry": http://oakroadsystems.com/math/

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• CHAPTER 2: LIMITS AND CONTINUITY

• CORRECTION to Page 2.1.14: The answer (limit value) for Example 9 is 1.

• MINOR CORRECTION to Page 2.5.8: The last Limit Form more precisely yields 0+.

BIG FILES: Chapter 2A (pdf)Chapter 2B (pdf) (typed; last revised 7/12/12)

SMALLER FILES (if you can’t get the big or medium files):

Section 2.1 (pdf): An Introduction to Limits (typed; last revised 7/12/12)

Section 2.2 (pdf): Properties of Limits (typed; last revised 7/12/12)

Section 2.3 (pdf): Limits and Infinity I (typed; last revised 7/12/12)

Section 2.4 (pdf): Limits and Infinity II (typed; last revised 7/12/12)

Section 2.5 (pdf): The Indeterminate Forms 0/0 and inf/inf (typed; last revised 7/12/12)

Section 2.6 (pdf): The Squeeze (Sandwich) Theorem (typed; last revised 7/12/12)

Section 2.7 (pdf): Precise Definitions of Limits (typed; last revised 7/12/12)

Section 2.8 (pdf): Continuity (typed; last revised 7/12/12)

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ARCHIVE OF OLD HANDWRITTEN NOTES BASED ON SWOKOWSKI’S CLASSIC EDITION

CHAPTER 1: REVIEW

Trig handouts:

1.3 Handout on Trig Identities (Part 1; I will hand this out in class.)

1.3 Handout on Trig Identities (Part 2; I will hand this out in class.)

CHAPTER 2: LIMITS AND CONTINUITY (EXPERIMENTAL TYPED NOTES)

Section 2.1 (pdf): Intro to Limits

Section 2.2 (pdf): Defining Limits

Section 2.3 (pdf): Finding Limits

Section 2.4 (pdf): Limits Involving Infinity

• SOME COMMENTS ON ASYMPTOTES AND HOLES:

Consider the graph of a function represented by y = f(x) in the standard xy-plane.

• We have a vertical asymptote (VA) at x=a if and only if f(x) approaches infinity or -infinity as x approaches a from the left or the right.

If f is a rational function, where f(x) is written as (polynomial)/(polynomial), then real zeros of the denominator correspond to VAs or holes (removable discontinuities). If c is a real zero of the denominator, and the limit form when x approaches c is of the form (nonzero real number)/0, then we have a VA at x = c. If, however, the limit form is 0/0, and the factors of the form (x-c) are completely canceled out in the denominator in the simplification process, then there is a removable discontinuity at x = c.

• We have a horizontal asymptote (HA) at y=L if and only if f(x) approaches L as x approaches infinity or -infinity. The graph of a rational function can have at most one HA; if there is a "long-run" limit in one direction, it must also be the long-run limit in the other direction.

Section 2.5 (pdf): Continuous Functions

• WHEN DOES f HAVE A JUMP DISCONTINUITY AT c? (2.5, A):

This happens if and only if the corresponding left-hand and right-hand limits exist, but they are unequal.

• NOTES ON IVT (2.5, D)

First sentence should end with "on [a,b]."