**MATH 150 - CALCULUS WITH ANALYTIC GEOMETRY
I**

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**¥ NOTES FOR CHAPTERS 0, 1, AND
2**

**(NOTATION GUIDE; 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 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 canÕt 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:**
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**

**¥ 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) É Chapter 2B (pdf) (typed; last revised
7/12/12)

**SMALLER
FILES (if you canÕt 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
SWOKOWSKIÕS 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*]."

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