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Classroom Resource Materials : (Record no. 79811)

MARC details
000 -LEADER
fixed length control field 07929nam a22004693i 4500
001 - CONTROL NUMBER
control field EBC3330355
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240729125049.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m o d |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cnu||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240724s2013 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781614441106
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9780883857816
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC3330355
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL3330355
035 ## - SYSTEM CONTROL NUMBER
System control number (CaPaEBR)ebr10722466
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)847680790
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA303.2.K59 2013eb
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Klymchuk, Sergiy.
245 10 - TITLE STATEMENT
Title Classroom Resource Materials :
Remainder of title Paradoxes and Sophisms in Calculus.
250 ## - EDITION STATEMENT
Edition statement 1st ed.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Providence :
Name of producer, publisher, distributor, manufacturer American Mathematical Society,
Date of production, publication, distribution, manufacture, or copyright notice 2013.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2013.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (113 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note cover -- copyright page -- title page -- Contents -- Introduction -- Acknowledgments -- I Paradoxes -- Functions and Limits -- Laying bricks -- Spiral curves -- A paradoxical fractal curve: the Koch snowflake -- A tricky fractal area: the Sierpinski carpet -- A mysterious fractal set: the Cantor ternary set -- A misleading sequence -- Remarkable symmetry -- Rolling a barrel -- A cat on a ladder -- Sailing -- Encircling the Earth -- A tricky equation -- A snail on a rubber rope -- Derivatives and Integrals -- An alternative product rule -- Missing information? -- A paint shortage -- Racing marbles -- A paradoxical pair of functions -- An unruly function -- Jagged peaks galore -- Another paradoxical pair of functions -- II Sophisms -- Functions and Limits -- Evaluation of lim_n _k=1n1n2+k proves that 1=0. -- Evaluation of lim_x0 (xsin1x ) proves that 1 = 0. -- Evaluation of lim_x0+ (xx) shows that 1 = 0. -- Evaluation of lim_n [n]n demonstrates that 1=. -- Trigonometric limits prove that sinkx = k sinx. -- Evaluation of a limit of a sum proves that 1=0. -- Analysis of the function x+yx-y proves that 1 = -1. -- Analysis of the function ax+yx+ay proves that a = 1a, for any value a 0. -- One-to-one correspondences imply that 1 = 2. -- Aristotle's wheel implies that R = r. -- Logarithmic inequalities show 2 &gt -- 3. -- Analysis of the logarithm function implies 2 &gt -- 3. -- Analysis of the logarithm function proves 14 &gt -- 12. -- Limit of perimeter curves shows that 2 = 1. -- Limit of perimeter curves shows = 2. -- Serret's surface area definition proves that = . -- Achilles and the tortoise -- Reasonable estimations lead to 1,000,000 2,000,000. -- Properties of square roots prove 1 = -1. -- Analysis of square roots shows that 2=-2. -- Properties of exponents show that 3 = -3. -- A slant asymptote proves that 2 = 1.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note Euler's interpretation of series shows 12 = 1-1+1-1+@let@token . -- Euler's manipulation of series proves -1&gt -- &gt -- 1. -- A continuous function with a jump discontinuity -- Evaluation of Taylor series proves ln2=0. -- Derivatives and Integrals -- Trigonometric integration shows 1 = C, for any real number C. -- Integration by parts demonstrates 1 = 0. -- Division by zero is possible. -- Integration proves sin2 x = 1 for any value of x. -- The u-substitution method shows that 2 &lt -- 0 &lt -- . -- ln2 is not defined. -- is not defined. -- Properties of indefinite integrals show 0=C, for any real number C. -- Volumes of solids of revolution demonstrate that 1 = 2. -- An infinitely fast fall -- A positive number equals a negative number. -- The power rule for differentiation proves that 2=1. -- III Solutions to Paradoxes -- Functions and Limits -- Laying bricks -- Spiral curves -- A paradoxical fractal curve: the Koch snowflake. -- A tricky fractal area: the Sierpinski carpet -- A mysterious fractal set: the Cantor ternary set -- A misleading sequence -- Remarkable symmetry: Reuleaux polygons -- Rolling a barrel -- A cat on a ladder -- Sailing -- Encircling the Earth -- A tricky equation -- A snail on a rubber rope -- Derivatives and Integrals -- An alternative product rule -- Missing information? -- A paint shortage -- Racing marbles -- A paradoxical pair of functions -- An unruly function -- Jagged peaks galore -- Another paradoxical pair of functions -- IV Solutions to Sophisms -- Functions and Limits -- Evaluation of lim_n n_k=1 1n2+k proves that 1 = 0. -- Evaluation of lim_x 0 ( xsin1x ) proves that 1 = 0. -- Evaluation of lim_x 0+ (xx) shows that 1 = 0. -- Evaluation of lim_n [n]n demonstrates that 1 = . -- Trigonometric limits prove that sinkx = ksinx. -- Evaluation of a limit of a sum proves that 1 = 0.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note Analysis of the function x + yx - y proves that 1 = -1. -- Analysis of the function ax + yx + ay proves that a = 1a, for any value a 0. -- One-to-one correspondences imply that 1 = 2. -- Aristotle's wheel implies that R = r. -- Logarithmic inequalities show 2 &gt -- 3. -- Analysis of the logarithm function implies 2 &gt -- 3. -- Analysis of the logarithm function proves 14 &gt -- 12. -- Limit of perimeter curves shows that 2 = 1. -- Limit of perimeter curves shows = 2. -- Serret's surface area definition proves that = . -- Achilles and the tortoise -- Reasonable estimations lead to 1,000,000 2,000,000. -- Properties of square roots prove 1 = -1. -- Analysis of square roots shows that 2 = -2. -- Properties of exponents show that 3=-3. -- A slant asymptote proves that 2=1. -- Euler's interpretation of series shows 12 = 1-1+1-1+@let@token . -- Euler's manipulation of series proves -1&gt -- &gt -- 1. -- A continuous function with a jump discontinuity. -- Evaluation of Taylor series proves ln2=0. -- Derivatives and Integrals -- Trigonometric Integration shows 1 = C, for any real number C. -- Integration by parts demonstrates 1 = 0. -- Division by zero is possible. -- Integration proves sin2 x = 1 for any value of x. -- The u-substitution method shows that 2 &lt -- 0 &lt -- . -- ln2 is not defined. -- is not defined. -- Properties of indefinite integrals show 0 = C, for any real number C. -- Volumes of solids of revolution demonstrate that 1 = 2. -- An infinitely fast fall -- A positive number equals a negative number. -- The power rule for differentiation proves that 2=1. -- Bibliography -- About the Authors.
520 ## - SUMMARY, ETC.
Summary, etc. Paradoxes and Sophisms in Calculus offers a delightful supplementary resource to enhance the study of single variable calculus. By the word paradox the authors mean a surprising, unexpected, counter-intuitive statement that looks invalid, but in fact is true. The word sophism describes intentionally invalid reasoning that looks formally correct, but in fact contains a subtle mistake or flaw. In other words, a sophism is a false proof of an incorrect statement. A collection of over fifty paradoxes and sophisms showcases the subtleties of this subject and leads students to contemplate the underlying concepts. A number of the examples treat historically significant issues that arose in the development of calculus, while others more naturally challenge readers to understand common misconceptions. Sophisms and paradoxes from the areas of functions, limits, derivatives, integrals, sequences, and series are explored.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Calculus.
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Staples, Susan.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Klymchuk, Sergiy
Title Classroom Resource Materials
Place, publisher, and date of publication Providence : American Mathematical Society,c2013
International Standard Book Number 9780883857816
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330355">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330355</a>
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