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
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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