Multivariable Calculus8th EditionJames Stewart Publisher: Cengage LearningISBN: 9781305266643
Multivariable Calculus
Solutions for Multivariable Calculus
Problem 1E:
(a) What is the difference between a sequence and a series? (b) What is a convergent series? What is...Problem 2E:
Explain what it means to say that n=1an=5.Problem 7E:
Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does...Problem 21E:
Determine whether the geometric series is convergent or divergent. If it is convergent, find its...Problem 23E:
Determine whether the geometric series is convergent or divergent. If it is convergent, find its...Problem 24E:
Determine whether the geometric series is convergent or divergent. If it is convergent, find its...Problem 34E:
Determine whether the series is convergent or divergent. If it is convergent, find its sum. 34....Problem 35E:
Determine whether the series is convergent or divergent. If it is convergent, find its sum. 35....Problem 41E:
Determine whether the series is convergent or divergent. If it is convergent, find its sum. 41....Problem 44E:
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in...Problem 45E:
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in...Problem 58E:
Find the values of x for which the series converges. Find the sum of the series for those values of...Problem 63E:
Find the values of x for which the series converges. Find the sum of the series for those values of...Problem 69E:
A doctor prescribes a 100-mg antibiotic tablet to be taken every eight hours. Just before each...Problem 70E:
A patient is injected with a drug every 12 hours. Immediately before each injection the...Problem 72E:
After injection of a dose D of insulin, the concentration of insulin in a patients system decays...Problem 73E:
When money is spent on goods and services, those who receive the money also spend some of it. The...Problem 74E:
A certain ball has the property that each time it falls from a height h onto a hard, level surface,...Problem 79E:
The figure shows two circles C and D of radius 1 that touch at P. The line T is a common tangent...Problem 80E:
A right triangle ABC is given with A = and |AC| = b. CD is drawn perpendicular to AB, DE is drawn...Problem 81E:
What is wrong with the following calculation?...Problem 89E:
The Cantor set, named after the German mathematician Georg Cantor (18451918), is constructed as...Browse All Chapters of This Textbook
Chapter 10 - Parametric Equations And Polar CoordinatesChapter 10.1 - Curves Defined By Parametric EquationsChapter 10.2 - Calculus With Parametric CurvesChapter 10.3 - Polar CoordinatesChapter 10.4 - Areas And Lengths In Polar CoordinatesChapter 10.5 - Conic SectionsChapter 10.6 - Conic Sections In Polar CoordinatesChapter 11 - Infinite Sequences And SeriesChapter 11.1 - SequencesChapter 11.2 - Series
Chapter 11.3 - The Integral Test And Estimates Of SumsChapter 11.4 - The Comparison TestsChapter 11.5 - Alternating SeriesChapter 11.6 - Absolute Convergence And The Ratio And Root TestsChapter 11.7 - Strategy For Testing SeriesChapter 11.8 - Power SeriesChapter 11.9 - Representations Of Functions As Power SeriesChapter 11.10 - Taylor And Maclaurin SeriesChapter 11.11 - Applications Of Taylor PolynomialsChapter 12 - Vectors And The Geometry Of SpaceChapter 12.1 - Three-dimensional Coordinate SystemsChapter 12.2 - VectorsChapter 12.3 - The Dot ProductChapter 12.4 - The Cross ProductChapter 12.5 - Equations Of Lines And PlanesChapter 12.6 - Cylinders And Quadric SurfacesChapter 13 - Vector FunctionsChapter 13.1 - Vector Functions And Space CurvesChapter 13.2 - Derivatives And Integrals Of Vector FunctionsChapter 13.3 - Arc Length And CurvatureChapter 13.4 - Motion In Space: Velocity And AccelerationChapter 14 - Partial DerivativesChapter 14.1 - Functions Of Several VariablesChapter 14.2 - Limits And ContinuityChapter 14.3 - Partial DerivativesChapter 14.4 - Tangent Planes And Linear ApproximationsChapter 14.5 - The Chain RuleChapter 14.6 - Directional Derivatives And The Gradient VectorChapter 14.7 - Maximum And Minimum ValuesChapter 14.8 - Lagrange MultipliersChapter 15 - Multiple IntegralsChapter 15.1 - Double Integrals Over RectanglesChapter 15.2 - Double Integrals Over General RegionsChapter 15.3 - Double Integrals In Polar CoordinatesChapter 15.4 - Applications Of Double IntegralsChapter 15.5 - Surface AreaChapter 15.6 - Triple IntegralsChapter 15.7 - Triple Integrals In Cylindrical CoordinatesChapter 15.8 - Triple Integrals In Spherical CoordinatesChapter 15.9 - Change Of Variables In Multiple IntegralsChapter 16 - Vector CalculusChapter 16.1 - Vector FieldsChapter 16.2 - Line IntegralsChapter 16.3 - The Fundamental Theorem For Line IntegralsChapter 16.4 - Green's TheoremChapter 16.5 - Curl And DivergenceChapter 16.6 - Parametric Surfaces And Their AreasChapter 16.7 - Surface IntegralsChapter 16.8 - Stokes' TheoremChapter 16.9 - The Divergence TheoremChapter 17 - Second-order Differential EquationsChapter 17.1 - Second-order Linear EquationsChapter 17.2 - Nonhomogeneous Linear EquationsChapter 17.3 - Applications Of Second-order Differential EquationsChapter 17.4 - Series SolutionsChapter G - Complex Numbers
Book Details
Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With MULTIVARIABLE CALCULUS, Eighth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course.
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