Solutions for Calculus: Early Transcendentals (2nd Edition)
Problem 3E:
Explain why a function that is not one-to-one on an interval I cannot have an inverse function on I.Problem 10E:
Express 25 using base e.Problem 11E:
One-to-one functions 11. Find three intervals on which f is one-to-one, making each interval as...Problem 12E:
Find four intervals on which f is one-to-one, making each interval as large as possible.Problem 13E:
Sketch a graph of a function that is one-to-one on the interval (, 0 ] but is not one-to-one on (,...Problem 14E:
Sketch a graph of a function that is one-to-one on the intervals (, 2], and [2, ) but is not...Problem 15E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 16E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 17E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 18E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 19E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 20E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 21E:
Finding inverse functions a. Find the inverse of each function (on the given interval, if specified)...Problem 25E:
Finding inverse functions a. Find the inverse of each function (on the given interval, if specified)...Problem 27E:
Finding inverse functions a. Find the inverse of each function (on the given interval, if specified)...Problem 29E:
Splitting up curves The unit circle x2 + y2 = 1 consists of four one-to-one functions, f1(x), f2(x),...Problem 30E:
Splitting up curves The equation y4 = 4x2 is associated with four one-to-one functions f1(x), f2(x),...Problem 31E:
Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph...Problem 36E:
Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph...Problem 47E:
Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the...Problem 48E:
Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the...Problem 49E:
Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the...Problem 50E:
Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the...Problem 51E:
Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the...Problem 52E:
Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the...Problem 57E:
Using inverse relations One hundred grams of a particular radioactive substance decays according to...Problem 59E:
Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a...Problem 60E:
Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a...Problem 61E:
Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a...Problem 62E:
Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a...Problem 63E:
Changing bases Convert the following expressions to the indicated base. 63. 2x using base eProblem 64E:
Changing bases Convert the following expressions to the indicated base. 64. 3sin x using base eProblem 65E:
Changing bases Convert the following expressions to the indicated base. 65. In |x| using base 5Problem 66E:
Changing bases Convert the following expressions to the indicated base. 66. log2 (x2 + 1) using base...Problem 67E:
Changing bases Convert the following expressions to the indicated base. 67. a1/ln a using base e,...Problem 68E:
Changing bases Convert the following expressions to the indicated base. 68. a1/log10a using base 10,...Problem 69E:
Explain why or why not Determine whether the following statements are true and give an explanation...Problem 70E:
Graphs of exponential functions The following figure shows the graphs of y = 2x, y = 3x, y = 2x, and...Problem 71E:
Graphs of logarithmic functions The following figure shows the graphs of y = log2 x, y = log4 x, and...Problem 72E:
Graphs of modified exponential functions Without using a graphing utility, sketch the graph of y =...Problem 73E:
Graphs of modified logarithmic functions Without using a graphing utility, sketch the graph of y =...Problem 74E:
Large intersection point Use any means to approximate the intersection point(s) of the graphs of...Problem 75E:
Finding all inverses Find all the inverses associated with the following functions and state their...Problem 77E:
Finding all inverses Find all the inverses associated with the following functions and state their...Problem 78E:
Finding all inverses Find all the inverses associated with the following functions and state their...Problem 79E:
Population model A culture of bacteria has a population of 150 cells when it is first observed. The...Problem 80E:
Charging a capacitor A capacitor is a device that stores electrical charge. The charge on a...Problem 81E:
Height and time The height in feet of a baseball hit straight up from the ground with an initial...Problem 82E:
Velocity of a skydiver The velocity of a skydiver (in m/s) t seconds after jumping from a plane is...Problem 88E:
Inverse of composite functions a. Let g(x) = 2x + 3 and h(x) = x3. Consider the composite function...Browse All Chapters of This Textbook
Chapter 1 - FunctionsChapter 1.1 - Review Of FunctionsChapter 1.2 - Representing FunctionsChapter 1.3 - Inverse, Exponential, And Logarithmic FunctionsChapter 1.4 - Trigonometric Functions And Their InversesChapter 2 - LimitsChapter 2.1 - The Idea Of LimitsChapter 2.2 - Definitions Of LimitsChapter 2.3 - Techniques For Computing LimitsChapter 2.4 - Infinite Limits
Chapter 2.5 - Limits At InfinityChapter 2.6 - ContinuityChapter 2.7 - Precise Definitions Of LimitsChapter 3 - DerivativesChapter 3.1 - Introducing The DerivativeChapter 3.2 - Working With DerivativesChapter 3.3 - Rules Of DifferentiationChapter 3.4 - The Product And Quotient RulesChapter 3.5 - Derivatives Of Trigonometric FunctionsChapter 3.6 - Derivatives As Rates Of ChangeChapter 3.7 - The Chain RuleChapter 3.8 - Implicit DifferentiationChapter 3.9 - Derivatives Of Logarithmic And Exponential FunctionsChapter 3.10 - Derivatives Of Inverse Trigonometric FunctionsChapter 3.11 - Related RatesChapter 4 - Applications Of The DerivativesChapter 4.1 - Maxima And MinimaChapter 4.2 - What Derivatives Tell UsChapter 4.3 - Graphing FunctionsChapter 4.4 - Optimization ProblemsChapter 4.5 - Linear Approximation And DifferentialsChapter 4.6 - Mean Value TheoremChapter 4.7 - L'hopital's RuleChapter 4.8 - Newton's MethodChapter 4.9 - AntiderivativesChapter 5 - IntegrationChapter 5.1 - Approximating Areas Under CurvesChapter 5.2 - Definite IntegralsChapter 5.3 - Fundamental Theorem Of CalculusChapter 5.4 - Working With IntegralsChapter 5.5 - Substitution RuleChapter 6 - Applications Of IntegrationChapter 6.1 - Velocity And Net ChangeChapter 6.2 - Regions Between CurvesChapter 6.3 - Volume By SlicingChapter 6.4 - Volume By ShellsChapter 6.5 - Length Of CurvesChapter 6.6 - Surface AreaChapter 6.7 - Physical ApplicationsChapter 6.8 - Logarithmic And Exponential Functions RevisitedChapter 6.9 - Exponential ModelsChapter 6.10 - Hyperbolic FunctionsChapter 7 - Integration TechniquesChapter 7.1 - Basic ApproachesChapter 7.2 - Integration By PartsChapter 7.3 - Trigonometric IntegralsChapter 7.4 - Trigonometric SubstitutionsChapter 7.5 - Partial FractionsChapter 7.6 - Other Integration StrategiesChapter 7.7 - Numerical IntegrationChapter 7.8 - Improper IntegralsChapter 7.9 - Introduction To Differential EquationsChapter 8 - Sequences And Infinite SeriesChapter 8.1 - An OverviewChapter 8.2 - SequencesChapter 8.3 - Infinite SeriesChapter 8.4 - The Divergence And Integral TestsChapter 8.5 - The Ratio, Root, And Comparison TestsChapter 8.6 - Alternating SeriesChapter 9 - Power SeriesChapter 9.1 - Approximating Functions With PolynomialsChapter 9.2 - Properties Of Power SeriesChapter 9.3 - Taylor SeriesChapter 9.4 - Working With Taylor SeriesChapter 10 - Parametric And Polar CurvesChapter 10.1 - Parametric EquationsChapter 10.2 - Polar CoordinatesChapter 10.3 - Calculus In Polar CoordinatesChapter 10.4 - Conic SectionsChapter 11 - Vectors And Vector-valued FunctionsChapter 11.1 - Vectors In The PlaneChapter 11.2 - Vectors In Three DimensionsChapter 11.3 - Dot ProductsChapter 11.4 - Cross ProductsChapter 11.5 - Lines And Curves In SpaceChapter 11.6 - Calculus Of Vector-valued FunctionsChapter 11.7 - Motion In SpaceChapter 11.8 - Length Of CurvesChapter 11.9 - Curvature And Normal VectorsChapter 12 - Functions Of Several VariablesChapter 12.1 - Planes And SurfacesChapter 12.2 - Graphs And Level CurvesChapter 12.3 - Limits And ContinuityChapter 12.4 - Partial DerivativesChapter 12.5 - The Chain RuleChapter 12.6 - Directional Derivatives And The GradientChapter 12.7 - Tangent Planes And Linear ApproximationChapter 12.8 - Maximum/minimum ProblemsChapter 12.9 - Lagrange MultipliersChapter 13 - Multiple IntegrationChapter 13.1 - Double Integrals Over Rectangular RegionsChapter 13.2 - Double Integrals Over General RegionsChapter 13.3 - Double Integrals In Polar CoordinatesChapter 13.4 - Triple IntegralsChapter 13.5 - Triple Integrals In Cylindrical And Spherical CoordinatesChapter 13.6 - Integrals For Mass CalculationsChapter 13.7 - Change Of Variables In Multiple IntegralsChapter 14 - Vector CalculusChapter 14.1 - Vector FieldsChapter 14.2 - Line IntegralsChapter 14.3 - Conservative Vector FieldsChapter 14.4 - Green's TheoremChapter 14.5 - Divergence And CurlChapter 14.6 - Surface IntegralsChapter 14.7 - Stokes' TheoremChapter 14.8 - Divergence TheoremChapter D1 - Differential EquationsChapter D1.1 - Basic IdeasChapter D1.2 - Direction Fields And Euler's MethodChapter D1.3 - Separable Differential EquationsChapter D1.4 - Special First-order Differential EquationsChapter D1.5 - Modeling With Differential EquationsChapter D2 - Second-order Differential EquationsChapter D2.1 - Basic IdeasChapter D2.2 - Linear Homogeneous EquationsChapter D2.3 - Linear Nonhomogeneous EquationsChapter D2.4 - ApplicationsChapter D2.5 - Complex Forcing FunctionsChapter A - Algebra Review
Book Details
This much anticipated second edition of the most successful new calculus text published in the last two decades retains the best of the first edition while introducing important advances and refinements. Authors Briggs, Cochran, and Gillett build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students' geometric intuition to introduce fundamental concepts, laying a foundation for the development that follows.
Sample Solutions for this Textbook
We offer sample solutions for Calculus: Early Transcendentals (2nd Edition) homework problems. See examples below:
Chapter 1, Problem 1REChapter 2, Problem 1REChapter 3, Problem 1REChapter 4, Problem 1REChapter 5, Problem 1REChapter 6, Problem 1REChapter 7, Problem 1REChapter 8, Problem 1REChapter 9, Problem 1RE
Chapter 10, Problem 1REChapter 11, Problem 1REExplanation: Given: The equation is 4x−3y=12 . Calculation: The graph of the given equation 4x−3y=12...Chapter 13, Problem 1REChapter 14, Problem 1REChapter D1, Problem 1REExplanation: Given: The differential equation is y″+2y′−ty=0 . The highest derivative occur in the...
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