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James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)
A five star textbook for college calculus
A five star textbook for college calculus
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Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
LIES MY CALCULATOR AND COMPUTER TOLD ME■ See Section 1.4 for a discussion ofgraphing calculators and computerswith graphing software.A wide variety of pocket-size calculating devices are currently marketed. Some can runprograms prepared by the user; some have preprogrammed packages for frequently usedcalculus procedures, including the display of graphs. All have certain limitations in common:a limited range of magnitude (usually less than for calculators) and a bound onaccuracy (typically eight to thirteen digits).A calculator usually comes with an owner’s manual. Read it! The manual will tell youabout further limitations (for example, for angles when entering trigonometric functions)and perhaps how to overcome them.Program packages for microcomputers (even the most fundamental ones, which realizearithmetical operations and elementary functions) often suffer from hidden flaws. You willbe made aware of some of them in the following examples, and you are encouraged toexperiment using the ideas presented here.10 100 1PRELIMINARY EXPERIMENTSWITH YOUR CALCULATOR OR COMPUTERTo have a first look at the limitations and quality of your calculator, make it compute 2 3.Of course, the answer is not a terminating decimal so it can’t be represented exactly onyour calculator. If the last displayed digit is 6 rather than 7, then your calculator approximates3 by truncating instead of rounding, so be prepared for slightly greater loss of accu-2racy in longer calculations.Now multiply the result by 3; that is, calculate 2 3 3. If the answer is 2, then subtract2 from the result, thereby calculating 2 3 3 2. Instead of obtaining 0 as theanswer, you might obtain a small negative number, which depends on the construction ofthe circuits. (The calculator keeps, in this case, a few “spare” digits that are rememberedbut not shown.) This is all right because, as previously mentioned, the finite number of digitsmakes it impossible to represent 2 3 exactly.A similar situation occurs when you calculate (s6) 2 6. If you do not obtain 0, theorder of magnitude of the result will tell you how many digits the calculator uses internally.Next, try to compute 1 5 using the y x key. Many calculators will indicate an errorbecause they are built to attempt e 5ln1 . One way to overcome this is to use the fact that1 k cos k whenever k is an integer.Calculators are usually constructed to operate in the decimal number system. In contrast,some microcomputer packages of arithmetical programs operate in a number systemwith base other than 10 (typically 2 or 16). Here the list of unwelcome tricks your devicecan play on you is even larger, since not all terminating decimal numbers are representedexactly. A recent implementation of the BASIC language shows (in double precision)examples of incorrect conversion from one number system into another, for example,Stewart: Calculus, Sixth Edition. ISBN: 0495011606. © 2008 Brooks/Cole. All rights reserved.whereas19 0.1 ? 1.90000 00000 00001Yet another implementation, apparently free of the preceding anomalies, will not calculatestandard functions in double precision. For example, the number, whoserepresentation with sixteen decimal digits should be 3.14159 26535 89793, appears as3.14159 29794 31152; this is off by more than 3 10 7 . What is worse, the cosine functionis programmed so badly that its “cos” 0 1 2 23 . (Can you invent a situation whenthis could ruin your calculations?) These or similar defects exist in other programminglanguages too.THE PERILS OF SUBTRACTION8 0.1 ? 0.79999 99999 99999 9 4 tan 1 1You might have observed that subtraction of two numbers that are close to each other is atricky operation. The difficulty is similar to this thought exercise: Imagine that you walkblindfolded 100 steps forward and then turn around and walk 99 steps. Are you sure thatyou end up exactly one step from where you started?Stewart: Calculus: Early Transcendentals, Seventh Edition. ISBN: 0538497904. (c) 2012 Brooks/Cole. All rights reserved.
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xiiPreface● Calculus: Concepts an
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xxPrefaceJoseph Stampfli, Indiana U
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Calculators, Computers, andOther Gr
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Diagnostic TestsSuccess in calculus
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2 a preview of calculusA¡A∞AA£A
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AQCR¨¨OFIGURE FOR PROBLEM 23P23.
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¨PA(¨) B(¨)QFIGURE for PROBLEM 2
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15. To construct the snowflake curv
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(b) Integrate the result of part (a
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792 Chapter 12 Vectors and the Geom
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Problems Plus 1. Each edge of a cub
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Copyright 2016 Cengage Learning. Al
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848 Chapter 13 Vector FunctionsIn g
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850 Chapter 13 Vector FunctionsThe
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882 chapter 13 Vector FunctionsEXER
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Problems Plus 1. A particle P moves
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Copyright 2016 Cengage Learning. Al
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888 Chapter 14 Partial DerivativesI
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Section 14.1 Functions of Several V
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894 Chapter 14 Partial Derivatives
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phy of Simpson on page 520.) The ex
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988 Chapter 15 Multiple IntegralsIn
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8. Show thaty`0arctan x 2 arctan xx
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1068 Chapter 16 Vector CalculusThe
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1070 Chapter 16 Vector CalculusIt a
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1072 Chapter 16 Vector Calculuszan
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1074 chapter 16 Vector Calculus15-1
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1102 Chapter 16 Vector CalculusCAS4
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1106 Chapter 16 Vector CalculusDiff
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1110 Chapter 16 Vector Calculus23-2
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1150 chapter 16 Vector Calculus;CAS
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6. The figure depicts the sequence
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1154 Chapter 17 Second-Order Differ
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1156 Chapter 17 Second-Order Differ
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A2appendix A Numbers, Inequalities,
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A4appendix A Numbers, Inequalities,
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A6appendix A Numbers, Inequalities,
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A8appendix A Numbers, Inequalities,
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A10appendix A Numbers, Inequalities
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A12appendix B Coordinate Geometry a
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A14appendix B Coordinate Geometry a
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A16appendix B Coordinate Geometry a
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A18appendix C Graphs of Second-Degr
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A20appendix C Graphs of Second-Degr
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A22appendix c Graphs of Second-Degr
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A24appendix D TrigonometryAnglesAng
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A26appendix D Trigonometryhypotenus
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A28appendix D TrigonometryTrigonome
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A30appendix D Trigonometry18a 18b18
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A32appendix D TrigonometryExercises
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A34appendix E Sigma NotationA conve
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A36appendix E Sigma NotationSOLUTIO
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A38appendix E Sigma NotationExercis
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A40appendix F Proofs of TheoremsSin
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A42appendix F Proofs of Theorems3
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A44appendix F Proofs of TheoremsDWe
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A46appendix F Proofs of TheoremsPro
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A48appendix F Proofs of TheoremsSec
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A50appendix G The Logarithm Defined
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A52appendix G The Logarithm Defined
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A56appendix G The Logarithm Defined
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A58appendix h Complex NumbersSOLUTI
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A60appendix h Complex NumbersThe po
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A62appendix h Complex NumbersFrom t
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A64appendix h Complex NumbersExerci
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A66 Appendix I Answers to Odd-Numbe
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