Calculus Volume 217th EditionGilbert Strang, Edwin Jed Herman Publisher: OpenStaxISBN: 9781938168062
Calculus Volume 2
Solutions for Calculus Volume 2
Problem 1E:
State whether the given sums are equal or unequal. i=110i and k=110k i=110i and i=615(i5) i=110i(i1)...Problem 2E:
In the following exercises, use the rules for sums of powers of integers to compute the sums. 2....Problem 3E:
In the following exercises, use the rules for sums of powers of integers to compute the sums. 3....Problem 4E:
Suppose that i=1100ai=15 and i=1100bi=12 . In the following exercises, compute the sums. 4....Problem 5E:
Suppose that i=1100ai=15 and i=1100bi=12 . In the following exercises, compute the sums. 5....Problem 6E:
Suppose that i=1100ai=15 and i=1100bi=12 . In the following exercises, compute the sums. 6....Problem 7E:
Suppose that i=1100ai=15 and i=1100bi=12 . In the following exercises, compute the sums. 7....Problem 8E:
In the following exercises, use summation properties and formulas to rewrite and evaluate the sums....Problem 9E:
In the following exercises, use summation properties and formulas to rewrite and evaluate the sums....Problem 10E:
In the following exercises, use summation properties and formulas to rewrite and evaluate the sums....Problem 11E:
In the following exercises, use summation properties and formulas to rewrite and evaluate the sums....Problem 12E:
Let Ln denote the left-endpoint sum using n subintervals and let Rn denote the corresponding...Problem 13E:
Let Ln denote the left-endpoint sum using n subintervals and let Rn denote the corresponding...Problem 14E:
Let Ln denote the left-endpoint sum using n subintervals and let Rn denote the corresponding...Problem 15E:
Let Ln denote the left-endpoint sum using n subintervals and let Rn denote the corresponding...Problem 16E:
Let Ln denote the left-endpoint sum using n subintervals and let Rn denote the corresponding...Problem 17E:
Let Ln denote the left-endpoint sum using n subintervals and let Rn denote the corresponding...Problem 18E:
Let Ln denote the left-endpoint sum using n subintervals and let Rn denote the corresponding...Problem 19E:
Let Ln denote the left-endpoint sum using n subintervals and let Rn denote the corresponding...Problem 20E:
Compute the left and right Riemann sums—L4 and R4, respectively—for f(x)=(2|x|) on [—2, 2]. Compute...Problem 21E:
Compute the left and right Riemann sums—L6 and R6, respectively—for f(x)=(3|3x|) on [0, 6]. Compute...Problem 22E:
Compute the left and right Riemann sums—L4 and R4, respectively—for f(x)=4x2 on [—2, 2] and compare...Problem 23E:
Compute the left and right Riemann sums—L6 and R6, respective1y—for f(x)=9(x3)2 on [0, 6] and...Problem 24E:
Express the following endpoint sums in sigma notation but do not evaluate them. 24. L30 for f(x)=x2...Problem 25E:
Express the following endpoint sums in sigma notation but do not evaluate them. 25. L10 for f(x)=4x2...Problem 26E:
Express the following endpoint sums in sigma notation but do not evaluate them. 26. R20 for f(x) =...Problem 27E:
Express the following endpoint sums in sigma notation but do not evaluate them. 27. R100 for Inx on...Problem 28E:
In the following exercises, graph the function then use a calculator or a computer program to...Problem 29E:
In the following exercises, graph the function then use a calculator or a computer program to...Problem 30E:
In the following exercises, graph the function then use a calculator or a computer program to...Problem 31E:
In the following exercises, graph the function then use a calculator or a computer program to...Problem 32E:
In the following exercises, graph the function then use a calculator or a computer program to...Problem 33E:
In the following exercises, graph the function then use a calculator or a computer program to...Problem 34E:
Let tj denote the time that it took Tejay van Garteren to ride the jth stage of the Tour de France...Problem 35E:
Let rj denote the total rainfall in Portland on the jth day of the year in 2009. Interpret j=131rj .Problem 36E:
Let dj denote the hours of daylight and j denote the increase in the hours of daylight from day j —...Problem 37E:
To help get in shape, Joe gets a new pair of running shoes. If Joe runs 1 mi each day in week 1 and...Problem 38E:
The following table gives approximate values of the average annual atmospheric rate of increase in...Problem 39E:
The following table gives the approximate increase in sea level in inches over 20 years starting in...Problem 40E:
The following table gives the approximate increase in dollars in the average price of a gallon of...Problem 41E:
The following {able gives the percent growth of the U.S. population beginning in July of the year...Problem 42E:
wIn the following exercises, estimate the areas under the curves by computing the left Riemann sums,...Problem 43E:
In the following exercises, estimate the areas under the curves by computing the left Riemann sums,...Problem 44E:
In the following exercises, estimate the areas under the curves by computing the left Riemann sums,...Problem 45E:
In the following exercises, estimate the areas under the curves by computing the left Riemann sums,...Problem 46E:
[T] Use a computer algebra system to compute the Riemann sum, LN, for N = 10. 30, 50 for f(x)=1x2 on...Problem 47E:
[T] Use a computer algebra system to computer the Riemann sum, LN, for N = 10, 30, 50 for f(x)=11x2...Problem 48E:
[T] Use a computer algebra system to compute the Riemann sum, LN, for N = 10, 30, 50 for f(x] =...Problem 49E:
In the following exercises, use a calculator or a computer program to evaluate the endpoint sums RN...Problem 50E:
In the following exercises, use a calculator or a computer program to evaluate the endpoint sums RN...Problem 51E:
In the following exercises, use a calculator at a computer program to evaluate the endpoint sums RN...Problem 52E:
In the following exercises, use a calculator at a computer program to evaluate the endpoint sums RN...Problem 53E:
In the following exercises, use a calculator at a computer program to evaluate the endpoint sums RN...Problem 54E:
In the following exercises, use a calculator at a computer program to evaluate the endpoint sums RN...Problem 55E:
In the following exercises, use a calculator at a computer program to evaluate the endpoint sums RN...Problem 56E:
In the following exercises, use a calculator at a computer program to evaluate the endpoint sums RN...Problem 57E:
For each Of the three graphs: a. Obtain a lower bound L(A) far the area enclosed by the curve by...Browse All Chapters of This Textbook
Chapter 1 - IntegrationChapter 1.1 - Approximating AreasChapter 1.2 - The Definite IntegralChapter 1.3 - The Fundamental Theorem Of CalculusChapter 1.4 - Integration Formulas And The Net Change TheoremChapter 1.5 - SubstitutionChapter 1.6 - Integrals Involving Exponential And Logarithmic FunctionsChapter 1.7 - Integrals Resulting In Inverse Trigonometric FunctionsChapter 2 - Applications Of IntegrationChapter 2.1 - Areas Between Curves
Chapter 2.2 - Determining Volumes By SlicingChapter 2.3 - Volumes Of Revolution: Cylindrical ShellsChapter 2.4 - Am Length Of A Curve And Surface AreaChapter 2.5 - Physical ApplicationsChapter 2.6 - Moments And Centers Of MassChapter 2.7 - Integrals, Exponential Functions, And LogarithmsChapter 2.8 - Exponential Growth And DecayChapter 2.9 - Calculus Of The Hyperbolic FunctionsChapter 3 - Techniques Of IntegrationChapter 3.1 - Integration By PartsChapter 3.2 - Trigonometric IntegralsChapter 3.3 - Trigonometric SubstitutionChapter 3.4 - Partial FractionsChapter 3.5 - Other Strategies For IntegrationChapter 3.6 - Numerical IntegrationChapter 3.7 - Improper IntegralsChapter 4 - Introduction To Differential EquationsChapter 4.1 - Basics Of Differential EquationsChapter 4.2 - Direction Fields And Numerical MethodsChapter 4.3 - Separable EquationsChapter 4.4 - The Logistic EquationChapter 4.5 - First-order Linear EquationsChapter 5 - Sequences And SeriesChapter 5.1 - SequencesChapter 5.2 - Infinite SeriesChapter 5.3 - The Divergence And Integral TestsChapter 5.4 - Comparison TestsChapter 5.5 - Alternating SeriesChapter 5.6 - Ratio And Root TestsChapter 6 - Power SeriesChapter 6.1 - Power Series And FunctionsChapter 6.2 - Properties Of Power SeriesChapter 6.3 - Taylor And Maclaurin SeriesChapter 6.4 - Working With Taylor SeriesChapter 7 - Parametric Equations And Polar CoordinatesChapter 7.1 - Parametric EquationsChapter 7.2 - Calculus Of Parametric CurvesChapter 7.3 - Polar CoordinatesChapter 7.4 - Area And Arc Length In Polar CoordinatesChapter 7.5 - Conic Sections
Book Details
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.
Sample Solutions for this Textbook
We offer sample solutions for Calculus Volume 2 homework problems. See examples below:
More Editions of This Book
Corresponding editions of this textbook are also available below:
Calculus Volume 2 by OpenStax
17th Edition
ISBN: 9781506698076
Calculus Volume 2
2nd Edition
ISBN: 9781630182021
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