## Solutions for Calculus: Early Transcendentals (3rd Edition)

Problem 1QC:

If f(x)=x22x, find f(1),f(x2),f(t), and f(p1).Problem 2QC:

State the domain and range of f(x)=(x2+1)1.Problem 3QC:

If f(x)=x2+1 and g(x)=x2, find fg and gf.Problem 4QC:

Refer to Figure 1.12. Find the hiker's average speed during the first mile of the trail and then...Problem 5QC:

Explain why the graph of a nonzero function is never symmetric with respect to the x-axis.Problem 1E:

Use the terms domain, range, independent variable, and dependent variable to explain how a function...Problem 2E:

Is the independent variable of a function associated with the domain or range? Is the dependent...Problem 5E:

Which statement about a function is true? (i) For each value of x in the domain, there corresponds...Problem 7E:

Determine the domain and range of f(x)=3x210.Problem 8E:

Domain in context Determine an appropriate domain of each function. Identify the independent and...Problem 9E:

Domain in context Determine an appropriate domain of each function. Identify the independent and...Problem 10E:

If f(x) = 1/(x3 + 1), what is f(2)? What is f(y2)?Problem 11E:

Let f(x)=2x+1 and g(x)=1/(x1). Simplify the expressions f(g(1/2)),g(f(4)), and g(f(x)).Problem 12E:

Find functions f and g such that f(g(x))=(x2+1)5. Find a different pair of functions and g that also...Problem 14E:

If f(x)=x and g(x)=x32, simplify the expressions (fg)(3),(ff)(64),(gf)(x), and (fg)(x).Problem 15E:

Composite functions from graphs Use the graphs of f and g in the figure to determine the following...Problem 16E:

Composite functions from tables Use the table to evaluate the given compositions. a. h(g(0)) b....Problem 17E:

Rising radiosonde The National Weather Service releases approximately 70,000 radiosondes every year...Problem 18E:

World record free fall On October 14, 2012, Felix Baumgartner stepped off a balloon capsule at an...Problem 19E:

Suppose f is an even function with f(2) = 2 and g is an odd function with g(2) = 2. Evaluate f(2),...Problem 22E:

Symmetry in graphs State whether the functions represented by graphs A, B, and C in the figure are...Problem 27E:

Domain State the domain of the function. 27.h(u)=u13Problem 28E:

Domain State the domain of the function. 28.F(w)=2w4Problem 31E:

Launching a rocket A small rocket is launched vertically upward from the edge of a cliff 80 ft off...Problem 32E:

Draining a tank (Torricellis law) A cylindrical tank with a cross-sectional area of 10 m2 is filled...Problem 33E:

Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or...Problem 34E:

Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or...Problem 35E:

Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or...Problem 36E:

Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or...Problem 37E:

Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or...Problem 38E:

Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or...Problem 39E:

Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or...Problem 40E:

Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or...Problem 41E:

Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or...Problem 42E:

Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or...Problem 43E:

Working with composite functions Find possible choices for outer and inner functions f and g such...Problem 44E:

Working with composite functions Find possible choices for outer and inner functions f and g such...Problem 45E:

Working with composite functions Find possible choices for outer and inner functions f and g such...Problem 46E:

Working with composite functions Find possible choices for outer and inner functions f and g such...Problem 47E:

More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x) = 1/(x 2). Determine the...Problem 48E:

More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x) = 1/(x 2). Determine the...Problem 50E:

More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x) = 1/(x 2). Determine the...Problem 51E:

More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x) = 1/(x 2). Determine the...Problem 52E:

More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x)=1/(x2). Determine the...Problem 54E:

More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x) = 1/(x 2). Determine the...Problem 55E:

Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 49. (f ...Problem 56E:

Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 50....Problem 57E:

Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 51. (f ...Problem 58E:

Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 52. (f ...Problem 59E:

Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 53. (g ...Problem 60E:

Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 54. (g ...Problem 61E:

Explain why or why not Determine whether the following statements are true and give an explanation...Problem 62E:

Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following...Problem 63E:

Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following...Problem 64E:

Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following...Problem 65E:

Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following...Problem 66E:

Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following...Problem 67E:

Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following...Problem 68E:

Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following...Problem 69E:

Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following...Problem 70E:

Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following...Problem 71E:

Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following...Problem 72E:

Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following...Problem 73E:

Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following...Problem 74E:

Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following...Problem 75E:

GPS data A GPS device tracks the elevation E (in feet) of a hiker walking in the mountains. The...Problem 76E:

Elevation vs. Distance The following graph, obtained from GPS data, shows the elevation of a hiker...Problem 77E:

Interpreting the slope of secant lines In each exercise, a function and an interval of its...Problem 78E:

Interpreting the slope of secant lines In each exercise, a function and an interval of its...Problem 79E:

Symmetry Determine whether the graphs of the following equations and functions are symmetric about...Problem 80E:

Symmetry Determine whether the graphs of the following equations and functions are symmetric about...Problem 81E:

Symmetry Determine whether the graphs of the following equations and functions are symmetric about...Problem 82E:

Symmetry Determine whether the graphs of the following equations and functions are symmetric about...Problem 85E:

Symmetry Determine whether the graphs of the following equations and functions are symmetric about...Problem 86E:

Symmetry Determine whether the graphs of the following equations and functions are symmetric about...Problem 87E:

Composition of even and odd functions from graphs Assume f is an even function and g is an odd...Problem 88E:

Composition of even and odd functions from tables Assume f is an even function and g is an odd...Problem 89E:

Absolute value graph Use the definition of absolute value to graph the equation |x| |y| = 1. Use a...Problem 90E:

Graphing semicircles Show that the graph of f(x)=10+x2+10x9 is the upper half of a circle. Then...Problem 91E:

Graphing semicircles Show that the graph of g(x)=2x2+6x+16 is the lower half of a circle. Then...Problem 92E:

Even and odd at the origin a. If f(0) is defined and f is an even function, is it necessarily true...Problem 93E:

Polynomial calculations Find a polynomial f that satisfies the following properties. (Hint:...Problem 94E:

Polynomial calculations Find a polynomial f that satisfies the following properties. (Hint:...Problem 95E:

Polynomial calculations Find a polynomial f that satisfies the following properties. (Hint:...Problem 96E:

Polynomial calculations Find a polynomial f that satisfies the following properties. (Hint:...Problem 97E:

Difference quotients Simplify the difference quotients f(x+h)f(x)h and f(x)f(a)xa by rationalizing...Problem 98E:

Difference quotients Simplify the difference quotients f(x+h)f(x)h and f(x)f(a)xa by rationalizing...Problem 99E:

Difference quotients Simplify the difference quotients f(x+h)f(x)h and f(x)f(a)xa by rationalizing...Problem 100E:

Difference quotients Simplify the difference quotients f(x+h)f(x)h and f(x)f(a)xa by rationalizing...Problem 101E:

Combining even and odd functions Let E be an even function and O be an odd function. Determine the...Problem 102E:

Combining even and odd functions Let E be an even function and O be an odd function. Determine the...# 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 (3rd 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 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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