Calculus Volume 22nd EditionGilbert Strang, Edwin Jed Herman Publisher: OpenStax College.ISBN: 9781630182021
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
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
17th Edition
ISBN: 9781938168062
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