Elementary Calculus An Infinitesimal [2 ed.]

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Elementary Calculus An Infinitesimal [2 ed.]

Author / Uploaded
H. Jerome Keisler

Categories
Mathematics

Table of contents :
Preface
Table of Contents
Introduction
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Epilogue
Appendix
Index
Cover Material

Citation preview

Dedicated to my sons, Randall, Jeffrey, and Thomas

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-sa/2.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California, 93405, USA.

Copyright © 2000 by H. Jerome Keisler. Revised August 2010 Revised February 2012 Revised May, 2009

1.3

(4),

(3, 1).

1

1/9.

(3,1),

|st(b)| > 0

With a calculator, compute some values as x approaches its limit, and see what happens.

have

Note: our proof used the fact that f has a maximum and minimum on each closed interval. That fact, called the Extreme Value Theorem, is proved on page 164.

With a calculator, compute some values as x approaches its limit, and see what happens.

With a calculator, the student should try this for some of the limits on pages 124 and 241.

Then check your answer by using a graphics calculator to draw the graph.

F(0,1/4a)

1/(4a). Its

d = 1/4a.

a=1/4d,

d=1/4a

y = --(1/2) 1/2 and d =1/4a

1/4a

1/4a), 1/4a.

1/4a.

+ 1/4a)

(0,1/4a),

1/4a=

1/4a.

9/16

Boyer, p. 217. Boyer, p. 217.

| |

3/4

40

y