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Calculus: Early Transcendentals

8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781285741550

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Chapter

Section

Problem 2E:

If f(x)=x2xx1andg(x)=x is it true that f = g?

Problem 3E:

The graph of a function f is given. (a) State the value of f(1). (b) Estimate the value of f(1). (c)...

Problem 4E:

The graphs of f and g are given. (a) State the values of f(4) and g(3). (b) For what values of x is...

Problem 5E:

Figure 1 was recorded by an instrument operated by the California Department of Mines and Geology at...

Problem 7E:

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of...

Problem 8E:

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of...

Problem 9E:

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of...

Problem 10E:

Problem 11E:

Shown is a graph of the global average temperature T during the 20th century. Estimate the...

Problem 12E:

Trees grow faster and form wider rings in warm years and grow more slowly and form narrower rings in...

Problem 13E:

You put some ice cubes in a glass, fill the glass with cold water, and then let the glass sit on a...

Problem 14E:

Three runners compete in a 100-meter race. The graph depicts the distance run as a function of time...

Problem 15E:

The graph shows the power consumption for a day in September in San Francisco. (P is measured in...

Problem 16E:

Sketch a rough graph of the number of hours of daylight as a function of the time of year.

Problem 17E:

Sketch a rough graph of the outdoor temperature as a function of time during a typical spring day.

Problem 18E:

Sketch a rough graph of the market value of a new car as a function of time for a period of 20...

Problem 19E:

Sketch the graph of the amount of a particular brand of coffee sold by a store as a function of the...

Problem 20E:

You place a frozen pie in an oven and bake it for an hour. Then you take it out and let it cool...

Problem 21E:

A homeowner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass...

Problem 22E:

An airplane takes off from an airport and lands an hour later at another airport, 400 miles away. If...

Problem 23E:

Temperature readings T (in F) were recorded every two hours from midnight to 2:00 PM in Atlanta on...

Problem 24E:

Researchers measured the blood alcohol concentration (BAC) of eight adult male subjects after rapid...

Problem 25E:

If f(x) = 3x2 x + 2, find f(2), f(2), f(a), f(a), f(a + 1), 2f(a), f(2a), f(a2), [f(a)]2, and f(a +...

Problem 26E:

A spherical balloon with radius r inches has volume V(r)=43r3. Find a function that represents the...

Problem 29E:

Evaluate the difference quotient for the given function. Simplify your answer. 29. f(x)=1x,...

Problem 30E:

Evaluate the difference quotient for the given function. Simplify your answer. 30. f(x)=x+3x+1,...

Problem 31E:

Find the domain of the function. 31. f(x)=x+4x29

Problem 32E:

Find the domain of the function. 32. f(x)=2x35x2+x6

Problem 33E:

Find the domain of the function. 33. f(t)=2t13

Problem 34E:

Find the domain of the function. 34. g(t)=3t2+t

Problem 35E:

Find the domain of the function. 35. h(x)=1x25x4

Problem 36E:

Find the domain of the function. 36. f(u)=u+11+1u+1

Problem 37E:

Find the domain of the function. 37. F(p)=2p

Problem 41E:

Evaluate f(3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the...

Problem 42E:

Evaluate f(3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the...

Problem 43E:

Evaluate f(3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the...

Problem 44E:

Evaluate f(3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the...

Problem 45E:

Sketch the graph of the function. 45. f(x) = x + |x|

Problem 46E:

Sketch the graph of the function. 46. f(x) = |x + 2|

Problem 47E:

Sketch the graph of the function. 47. g(t) = |1 3t|

Problem 50E:

Sketch the graph of the function. 50. g(x) = ||x| 1|

Problem 51E:

Find an expression for the function whose graph is the given curve. 51. The line segment joining the...

Problem 52E:

Find an expression for the function whose graph is the given curve. 52. The line segment joining the...

Problem 53E:

Find an expression for the function whose graph is the given curve. 53. The bottom half of the...

Problem 54E:

Find an expression for the function whose graph is the given curve. 54. The top half of the circle...

Problem 57E:

Find a formula for the described function and state its domain. 57. A rectangle has perimeter 20 m....

Problem 58E:

Find a formula for the described function and state its domain. 58. A rectangle has area 16 m2....

Problem 59E:

Find a formula for the described function and state its domain. 59. Express the area of an...

Problem 60E:

Find a formula for the described function and state its domain. 60. A closed rectangular box with...

Problem 61E:

Find a formula for the described function and state its domain. 61. An open rectangular box with...

Problem 62E:

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the...

Problem 63E:

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12...

Problem 64E:

A cell phone plan has a basic charge of 35 a month. The plan includes 400 free minutes and charges...

Problem 65E:

In a certain state the maximum speed permitted on freeways is 65 mi/h and the minimum speed is 40...

Problem 66E:

An electricity company charges its customers a base rate of 10 a month, plus 6 cents per...

Problem 67E:

In a certain country, income tax is assessed as follows. There is no tax on income up to10,000. Any...

Problem 68E:

The functions in Example 10 and Exercise 67 are called step function because their graphs look like...

Problem 69E:

Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your...

Problem 70E:

Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your...

Problem 71E:

(a) If the point (5, 3) is on the graph of an even function, what other point must also be on the...

Problem 72E:

A function f has domain [5, 5] and a portion of its graph is shown. (a) Complete the graph of f if...

Problem 73E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

Problem 74E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

Problem 75E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

Problem 76E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

Problem 77E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

Problem 78E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

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Chapter 1 - Functions And ModelsChapter 1.1 - Four Ways To Represent A FunctionChapter 1.2 - Mathematical Models: A Catalog Of Essential FunctionsChapter 1.3 - New Functions From Old FunctionsChapter 1.4 - Exponential FunctionsChapter 1.5 - Inverse Functions And LogarithmsChapter 2 - Limits And DerivativesChapter 2.1 - The Tangent And Velocity ProblemsChapter 2.2 - The Limit Of A FunctionChapter 2.3 - Calculating Limits Using The Limit Laws

Chapter 2.4 - The Precise Definition Of A LimitChapter 2.5 - ContinuityChapter 2.6 - Limits At Infinity; Horizontal AsymptotesChapter 2.7 - Derivatives And Rates Of ChangeChapter 2.8 - The Derivative As A FunctionChapter 3 - Differentiation RulesChapter 3.1 - Derivatives Of Polynomials And Exponential FunctionsChapter 3.2 - The Product And Quotient RulesChapter 3.3 - Derivatives Of Trigonometric FunctionsChapter 3.4 - The Chain RuleChapter 3.5 - Implicit DifferentiationChapter 3.6 - Derivatives Of Logarithmic FunctionsChapter 3.7 - Rates Of Change In The Natural And Social SciencesChapter 3.8 - Exponential Growth And DecayChapter 3.9 - Related RatesChapter 3.10 - Linear Approximations And DifferentialsChapter 3.11 - Hyperbolic FunctionsChapter 4 - Applications Of DifferentiationChapter 4.1 - Maximum And Minimum ValuesChapter 4.2 - The Mean Value TheoremChapter 4.3 - How Derivatives Affect The Shape Of A GraphChapter 4.4 - Indeterminate Forms And L'hospital's RuleChapter 4.5 - Summary Of Curve SketchingChapter 4.6 - Graphing With Calculus And CalculatorsChapter 4.7 - Optimization ProblemsChapter 4.8 - Newton's MethodChapter 4.9 - AntiderivativesChapter 5 - IntegralsChapter 5.1 - Areas And DistancesChapter 5.2 - The Definite IntegralChapter 5.3 - The Fundamental Theorem Of CalculusChapter 5.4 - Indefinite Integrals And The Net Change TheoremChapter 5.5 - The Substitution RuleChapter 6 - Applications Of IntegrationChapter 6.1 - Areas Between CurvesChapter 6.2 - VolumesChapter 6.3 - Volumes By Cylindrical ShellsChapter 6.4 - WorkChapter 6.5 - Average Value Of A FunctionChapter 7 - Techniques Of IntegrationChapter 7.1 - Integration By PartsChapter 7.2 - Trigonometric IntegralsChapter 7.3 - Trigonometric SubstitutionChapter 7.4 - Integration Of Rationai Functions By Partial FractionsChapter 7.5 - Strategy For IntegrationChapter 7.6 - Integration Using Tables And Computer Algebra SystemsChapter 7.7 - Approximate IntegrationChapter 7.8 - Improper IntegralsChapter 8 - Further Applications Of IntegrationChapter 8.1 - Arc LengthChapter 8.2 - Area Of A Surface Of RevolutionChapter 8.3 - Applications To Physics And EngineeringChapter 8.4 - Applications To Economics And BiologyChapter 8.5 - ProbabilityChapter 9 - Differential EquationsChapter 9.1 - Modeling With Differential EquationsChapter 9.2 - Direction Fields And Euler's MethodChapter 9.3 - Separable EquationsChapter 9.4 - Models For Population GrowthChapter 9.5 - Linear EquationsChapter 9.6 - Predator-prey SystemsChapter 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 - SeriesChapter 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 Solutions

Success in your calculus course starts here! James Stewart's CALCULUS: EARLY TRANSCENDENTALS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: EARLY TRANSCENDENTALS, 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.

We offer sample solutions for Calculus: Early Transcendentals homework problems. See examples below:

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(a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...Explain what each of the following means and illustrate with sketch. (a) limxaf(x)=L (b)...State each differentiation rule both in symbols and in words. (a) The Power Rule (b) The Constant...Explain the difference between an absolute maximum and a local maximum. Illustrate with a sketch.(a) Write an expression for a Riemann sum of a function f. Explain the meaning of the notation that...(a) Draw two typical curves y = f(x) and y = g(x), where f(x) g(x) for a x b. Show how to...Stale the rule for integration by parts. In practice, how do you use it?(a) How is the length of a curve defined? (b) Write an expression for the length of a smooth curve...(a) What is a differential equation? (b) What is the order of a differential equation? (c) What is...

(a) What is a parametric curve? (b) How do you sketch a parametric curve?(a) What is a convergent sequence? (b) What is a convergent series? (c) What does limnan= 3 mean?...What is the difference between a vector and a scalar?What is a vector function? How do you find its derivative and its integral?(a) What is a function of two variables? (b) Describe three methods for visualizing a function of...Suppose f is a continuous function defined on a rectangle R = [a, b] [c, d]. (a) Write an...What is a vector field? Give three examples that have physical meaning.(a) Write the general form of a second-order homogeneous linear differential equation with constant...

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