MATH 150 - CALCULUS WITH ANALYTIC GEOMETRY I

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¥ NOTES FOR CHAPTERS 1 AND 2

(REVIEW; LIMITS AND CONTINUITY)

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TABLE OF CONTENTS (relevant from Ch.3 on)

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 1: REVIEW

BIG FILE: Chapter 1 (pdf): Review (last revised 7/28/09)

SMALLER FILES (if you canÕt get the big files):

Topic 1 (pdf): Functions (last revised 1/15/09)

Topic 2 (pdf): Trigonometry I (last revised 1/15/09)

Topic 3 (pdf): Trigonometry II (last revised 7/28/09)

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: http://www.purplemath.com

¥ Trig site with Java applets to play with!: http://www.catcode.com/trig

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

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¥ CHAPTER 2: LIMITS AND CONTINUITY

BIG FILE: Chapter 2 (pdf): Limits and Continuity (last revised 8/21/11)

CORRECTION TO BOOKSTORE COPIES: Warning about DTS (2.3)

Delete Page 2.3.26 of the bookstore copies. We shouldnÕt factor pieces of the numerator and the denominator and eliminate Òlocal factorsÓ as we take limits, because they could have a real impact on the overall limit.

CORRECTION: Page 2.6.9: Replace the first x2 with x.

MEDIUM PDF FILES: Chapter 2A (pdf) É Chapter 2B (pdf)

SMALLER FILES (if you canÕt get the big or medium files):

Section 2.1 (pdf): An Introduction to Limits (last revised 8/21/11)

Section 2.2 (pdf): Properties of Limits (last revised 8/21/11)

Section 2.3 (pdf): Limits and Infinity I (last revised 8/21/11)

CORRECTION FOR 2.3: Warning about DTS (2.3)

Delete Page 2.3.26. We shouldnÕt factor pieces of the numerator and the denominator and eliminate Òlocal factorsÓ as we take limits, because they could have a real impact on the overall limit.

Section 2.4 (pdf): Limits and Infinity II (last revised 8/21/11)

Section 2.5 (pdf): The Indeterminate Forms 0/0 and inf/inf (last revised 8/21/11)

Section 2.6 (pdf): The Squeeze (Sandwich) Theorem (last revised 8/8/09)

CORRECTION: Page 2.6.9: Replace the first x2 with x.

Section 2.7 (pdf): Precise Definitions of Limits (last revised 8/21/11)

Section 2.8 (pdf): Continuity (last revised 8/21/11)

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ARCHIVE OF OLD HANDWRITTEN NOTES BASED ON SWOKOWSKIÕS CLASSIC EDITION

CHAPTER 1: REVIEW

Chapter 1 (pdf)

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]."

Chapters 1 and 2 Review

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