CALCULUS, VOLUME 1 (OER)17th EditionOpenStax Publisher: XANEDU CISBN: 2810022307715
CALCULUS, VOLUME 1 (OER)
Solutions for CALCULUS,VOLUME 1 (OER)
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 sub intervals and let Rn denote the corresponding...Problem 13E:
Let Ln denote the left-endpoint sum using n sub intervals and let Rn denote the corresponding...Problem 14E:
Let Ln denote the left-endpoint sum using n sub intervals and let Rn denote the corresponding...Problem 15E:
Let Ln denote the left-endpoint sum using n sub intervals and let Rn denote the corresponding...Problem 16E:
Let Ln denote the left-endpoint sum using n sub intervals and let Rn denote the corresponding...Problem 17E:
Let Ln denote the left-endpoint sum using n sub intervals and let Rn denote the corresponding...Problem 18E:
Let Ln denote the left-endpoint sum using n sub intervals and let Rn denote the corresponding...Problem 19E:
Let Ln denote the left-endpoint sum using n sub intervals and let Rn denote the corresponding...Problem 20E:
Compute the left and tight Riemann sums— L4 and R4 . espectively—for f(x)=(2|x|) on [-2, 2]. Compute...Problem 21E:
Compute the left and light Riemann sums— L6 and R6 , respectively—for f(x)=(3|3x|) on [0, 6]....Problem 22E:
Compute the left and light Riemann sums— L4 and R4 , respectively—for f(x)=4x2 on [-2, 2] and...Problem 23E:
Compute the left and right Riemann sums— L6 and R6 , respectively—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...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:
In the following exercises, graph the function then use a calculator or a computer program to...Problem 35E:
In the following exercises, graph the function then use a calculator or a computer program to...Problem 36E:
In the following exercises, graph the function then use a calculator or a computer program to...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 table gives the percent growth of the U.S. population beginning in July of the year...Problem 42E:
In 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...Problem 47E:
[T] Use a computer algebra system to compute the Riemann sum, LN, for N = 10, 30, 50 for f(x)=11+x2...Problem 48E:
[T] Use a computer algebra system to compute the Riemann sum, LN , for N = 10, 30, 50 for f(x)=sin2x...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 or a computer program to evaluate the endpoint sums RN...Problem 52E:
In the following exercises, use a calculator or a computer program to evaluate the endpoint sums RN...Problem 53E:
In the following exercises, use a calculator or a computer program to evaluate the endpoint sums RN...Problem 54E:
Explain why, if f(b)0 and f is decreasing on [a, b], that the left endpoint estimate is an upper...Problem 55E:
Show that, in general, RNLN=(ba)f(b)f(a)N .Problem 56E:
Explain why, if f is increasing on |a,b| , the error between either LN or RN and the area A below...Problem 57E:
For each of the three graphs: Obtain a lower bound L(A) for the area enclosed by the curve by adding...Browse All Chapters of This Textbook
Chapter 1 - Functions And GraphsChapter 1.1 - Review Of FunctionsChapter 1.2 - Basic Classes Of FunctionsChapter 1.3 - Trigonometric FunctionsChapter 1.4 - Inverse FunctionsChapter 1.5 - Exponential And Logarithmic FunctionsChapter 2 - LimitsChapter 2.1 - A Preview Of CalculusChapter 2.2 - The Limit Of A FunctionChapter 2.3 - The Limit Laws
Chapter 2.4 - ContinuityChapter 2.5 - The Precise Definition Of A LimitChapter 3 - DerivativesChapter 3.1 - Defining The DerivativeChapter 3.2 - The Derivative As A FunctionChapter 3.3 - Differentiation RulesChapter 3.4 - Derivatives As Rates Of ChangeChapter 3.5 - Derivatives Of Trigonometric FunctionsChapter 3.6 - The Chain RuleChapter 3.7 - Derivatives Of Inverse FunctionsChapter 3.8 - Implicit DifferentiationChapter 3.9 - Derivatives Of Exponential And Logarithmic FunctionsChapter 4 - Applications Of DerivativesChapter 4.1 - Related RatesChapter 4.2 - Linear Approximations And DifferentialsChapter 4.3 - Maxima And MinimaChapter 4.4 - The Mean Value TheoremChapter 4.5 - Derivatives And The Shape Of A GraphChapter 4.6 - Limits At Infinity And AsymptotesChapter 4.7 - Applied Optimization ProblemsChapter 4.8 - L'hopitars RuleChapter 4.9 - Newton's MethodChapter 4.10 - AntiderivativesChapter 5 - IntegrationChapter 5.1 - Approximating AreasChapter 5.2 - The Definite IntegralChapter 5.3 - The Fundamental Theorem Of CalculusChapter 5.4 - Integration Formulas And The Net Change TheoremChapter 5.5 - SubstitutionChapter 5.6 - Integrals Involving Exponential And Logarithmic FunctionsChapter 5.7 - Integrals Resulting In Inverse Trigonometric FunctionsChapter 6 - Applications Of IntegrationChapter 6.1 - Areas Between CurvesChapter 6.2 - Determining Volumes By SlicingChapter 6.3 - Volumes Of Revolution: Cylindrical ShellsChapter 6.4 - Arc Length Of A Curve And Surface AreaChapter 6.5 - Physical ApplicationsChapter 6.6 - Moments And Centers Of MassChapter 6.7 - Integrals, Exponential Functions, And LogarithmsChapter 6.8 - Exponential Growth And DecayChapter 6.9 - Calculus Of The Hyperbolic Functions
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