Solutions for CALCULUS: EARLY TRANSCENDENTALS (LCPO)
Problem 1QC:
Is it possible to raise a positive number b to a power and obtain a negative number? Is it possible...Problem 2QC:
Explain why f(x)=(13)x is a decreasing function.Problem 4QC:
The function that gives degrees Fahrenheit in terms of degrees Celsius is F = 9C/5 + 32. Why does...Problem 3E:
Sketch a graph of a function that is one-to-one on the interval (, 0 ] but is not one-to-one on (,...Problem 4E:
Sketch a graph of a function that is one-to-one on the intervals (, 2], and [2, ) but is not...Problem 5E:
One-to-one functions 11. Find three intervals on which f is one-to-one, making each interval as...Problem 6E:
Find four intervals on which f is one-to-one, making each interval as large as possible.Problem 7E:
Explain why a function that is not one-to-one on an interval I cannot have an inverse function on I.Problem 10E:
Find the inverse of the function f(x)=x, for x 0. Verify that f(f1(x))=x and f1(f(x))=x.Problem 13E:
The parabola y=x2+1 consists of two one-to-one functions, g1(x) and g2(x). Complete each exercise...Problem 14E:
The parabola y=x2+1 consists of two one-to-one functions, g1(x) and g2(x). Complete each exercise...Problem 15E:
Explain the meaning of logbx.Problem 18E:
Express 25 using base e.Problem 19E:
Evaluate each expression without a calculator. a. log101000 b. log216 c. log100.01 d. ln e3 e. ln eProblem 20E:
For a certain constant a 1, ln a 3.8067. Find approximate values of log2a and loga2 using the fact...Problem 21E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 22E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 23E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 24E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 25E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 26E:
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible...Problem 27E:
Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph...Problem 28E:
Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph...Problem 29E:
Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph...Problem 30E:
Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph...Problem 31E:
Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph...Problem 32E:
Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph...Problem 33E:
Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if...Problem 34E:
Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if...Problem 35E:
Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if...Problem 36E:
Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if...Problem 37E:
Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if...Problem 38E:
Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if...Problem 39E:
Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if...Problem 40E:
Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if...Problem 41E:
Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if...Problem 42E:
Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if...Problem 43E:
Splitting up curves The unit circle x2 + y2 = 1 consists of four one-to-one functions, f1(x), f2(x),...Problem 44E:
Splitting up curves The equation y4 = 4x2 is associated with four one-to-one functions f1(x), f2(x),...Problem 45E:
Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the...Problem 46E:
Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the...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 61E:
Using inverse relations One hundred grams of a particular radioactive substance decays according to...Problem 62E:
Mass of juvenile desert tortoises In a study conducted at the University of New Mexico, it was found...Problem 63E:
Investment Problems An investment of P dollars is deposited in a savings account that is compounded...Problem 64E:
Investment Problems An investment of P dollars is deposited in a savings account that is compounded...Problem 65E:
Height and time The height in feet of a baseball hit straight up from the ground with an initial...Problem 66E:
Velocity of a skydiver The velocity of a skydiver (in m/s) t seconds after jumping from a plane is...Problem 67E:
Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a...Problem 68E:
Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a...Problem 69E:
Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a...Problem 70E:
Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a...Problem 71E:
Changing bases Convert the following expressions to the indicated base. 63. 2x using base eProblem 72E:
Changing bases Convert the following expressions to the indicated base. 64. 3sin x using base eProblem 73E:
Changing bases Convert the following expressions to the indicated base. 65. In |x| using base 5Problem 74E:
Changing bases Convert the following expressions to the indicated base. 66. log2 (x2 + 1) using base...Problem 75E:
Changing bases Convert the following expressions to the indicated base. 67. a1/ln a using base e,...Problem 76E:
Changing bases Convert the following expressions to the indicated base. 68. a1/log10a using base 10,...Problem 77E:
Explain why or why not Determine whether the following statements are true and give an explanation...Problem 78E:
Graphs of exponential functions The following figure shows the graphs of y = 2x, y = 3x, y = 2x, and...Problem 79E:
Graphs of logarithmic functions The following figure shows the graphs of y = log2 x, y = log4 x, and...Problem 80E:
Graphs of modified exponential functions Without using a graphing utility, sketch the graph of y =...Problem 81E:
Graphs of modified logarithmic functions Without using a graphing utility, sketch the graph of y =...Problem 82E:
Population model A culture of bacteria has a population of 150 cells when it is first observed. The...Problem 83E:
Charging a capacitor A capacitor is a device that stores electrical charge. The charge on a...Problem 84E:
Large intersection point Use any means to approximate the intersection point(s) of the graphs of...Problem 85E:
Finding all inverses Find all the inverses associated with the following functions, and state their...Problem 86E:
Finding all inverses Find all the inverses associated with the following functions, and state their...Problem 87E:
Finding all inverses Find all the inverses associated with the following functions and state their...Problem 89E:
Finding all inverses Find all the inverses associated with the following functions and state their...Problem 90E:
Finding all inverses Find all the inverses associated with the following functions and state their...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 DerivativesChapter 3.2 - The Derivative As A FunctionChapter 3.3 - Rules Of DifferentiationChapter 3.4 - The Product And Quotient RulesChapter 3.5 - Derivatives Of Trigonometric FunctionsChapter 3.6 - Derivatives As A 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 DerivativeChapter 4.1 - Maxima And MinimaChapter 4.2 - Mean Value TheoremChapter 4.3 - What Derivative Tell UsChapter 4.4 - Graphing FunctionsChapter 4.5 - Optimization ProblemsChapter 4.6 - Linear Approximation And DifferentialsChapter 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 7 - Logarithmic And Exponential, And Hyperbolic FunctionsChapter 7.1 - Logarithmic And Exponential Functions RevisitedChapter 7.2 - Exponential ModelsChapter 7.3 - Hyperbolic FunctionsChapter 8 - Integration TechniquesChapter 8.1 - Basic ApproachesChapter 8.2 - Integration By PartsChapter 8.3 - Trigonometric IntegralsChapter 8.4 - Trigonometric SubstitutionsChapter 8.5 - Partial FractionsChapter 8.6 - Integration StrategiesChapter 8.7 - Other Methods Of IntegrationChapter 8.8 - Numerical IntegrationChapter 8.9 - Improper IntegralsChapter 9 - Differential EquationsChapter 9.1 - Basic IdeasChapter 9.2 - Direction Fields And Euler's MethodChapter 9.3 - Separable Differential EquationsChapter 9.4 - Special First-order Linear Differential EquationsChapter 9.5 - Modeling With Differential EquationsChapter 10 - Sequences And Infinite SeriesChapter 10.1 - An OverviewChapter 10.2 - SequencesChapter 10.3 - Infinite SeriesChapter 10.4 - The Divergence And Integral TestsChapter 10.5 - Comparison TestsChapter 10.6 - Alternating SeriesChapter 10.7 - The Ration And Root TestsChapter 10.8 - Choosing A Convergence TestChapter 11 - Power SeriesChapter 11.1 - Approximating Functions With PolynomialsChapter 11.2 - Properties Of Power SeriesChapter 11.3 - Taylor SeriesChapter 11.4 - Working With Taylor SeriesChapter 12 - Parametric And Polar CurvesChapter 12.1 - Parametric EquationsChapter 12.2 - Polar CoordinatesChapter 12.3 - Calculus In Polar CoordinatesChapter 12.4 - Conic SectionsChapter 13 - Vectors And The Geometry Of SpaceChapter 13.1 - Vectors In The PlaneChapter 13.2 - Vectors In Three DimensionsChapter 13.3 - Dot ProductsChapter 13.4 - Cross ProductsChapter 13.5 - Lines And Planes In SpaceChapter 13.6 - Cylinders And Quadric SurfacesChapter 14 - Vector-valued FunctionsChapter 14.1 - Vector-valued FunctionsChapter 14.2 - Calculus Of Vector-valued FunctionsChapter 14.3 - Motion In SpaceChapter 14.4 - Length Of CurvesChapter 14.5 - Curvature And Normal VectorsChapter 15 - Functions Of Several VariablesChapter 15.1 - Graphs And Level CurvesChapter 15.2 - Limits And ContinuityChapter 15.3 - Partial DerivativesChapter 15.4 - The Chain RuleChapter 15.5 - Directional Derivatives And The GradientChapter 15.6 - Tangent Planes And Linear ProblemsChapter 15.7 - Maximum/minimum ProblemsChapter 15.8 - Lagrange MultipliersChapter 16 - Multiple IntegrationChapter 16.1 - Double Integrals Over Rectangular RegionsChapter 16.2 - Double Integrals Over General RegionsChapter 16.3 - Double Integrals In Polar CoordinatesChapter 16.4 - Triple IntegralsChapter 16.5 - Triple Integrals In Cylindrical And Spherical CoordinatesChapter 16.6 - Integrals For Mass CalculationsChapter 16.7 - Change Of Variables In Multiple IntegralsChapter 17 - Vector CalculusChapter 17.1 - Vector FieldsChapter 17.2 - Line IntegralsChapter 17.3 - Conservative Vector FieldsChapter 17.4 - Green's TheoremChapter 17.5 - Divergence And CurlChapter 17.6 - Surface IntegralsChapter 17.7 - Stokes' TheoremChapter 17.8 - Divergence TheoremChapter B - Algebra ReviewChapter C - Complex Numbers
Sample Solutions for this Textbook
We offer sample solutions for CALCULUS: EARLY TRANSCENDENTALS (LCPO) 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 1REChapter 12, Problem 1REChapter 13, Problem 1REThe given vector valued function is r(t)=〈cost,et,t〉+C. Substitute t=0 in the vector as follows....The given function is, g(x,y)=ex+y. Let ex+y=k. Take log on both sides. ex+y=kln(ex+y)=ln(k)x+y=lnk...Chapter 16, Problem 1REChapter 17, Problem 1REChapter B, Problem 1EChapter C, Problem 1E
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