## Solutions for Thomas' Calculus (14th Edition)

Problem 7E:

Which of the graphs are graphs of functions of x, and which are not? Give reasons for your...Problem 8E:

Which of the graphs are graphs of functions of x, and which are not? Give reasons for your...Problem 10E:

Express the side length of a square as a function of the length d of the square’s diagonal. Then...Problem 11E:

Express the edge length of a cube as a function of the cube’s diagonal length d. Then express the...Problem 12E:

A point P in the first quadrant lies on the graph of the function . Express the coordinates of P as...Problem 13E:

Consider the point (x, y) lying on the graph of the line 2x + 4y = 5. Let L be the distance from the...Problem 14E:

Consider the point (x, y) lying on the graph of . Let L be the distance between the points (x, y)...Problem 19E:

Functions and Graphs
Find the natural domain and graph the functions in Exercises 15–20.
19.
Problem 20E:

Functions and Graphs
Find the natural domain and graph the functions in Exercises 15–20.
20.
Problem 21E:

Find the domain of .
Problem 22E:

Find the range of .
Problem 23E:

Graph the following equations and explain why they are not graphs of functions of x.
|y| = x
y2 =...Problem 24E:

Graph the following equations and explain why they are not graphs of functions of x.
|x| + |y| =...Problem 25E:

Graph the functions in Exercise.
Problem 27E:

Graph the functions in Exercise.
Problem 33E:

For what values of x is
Problem 34E:

What real numbers x satisfy the equation
Problem 35E:

Does for all real x? Give reasons for your answer.
Problem 37E:

Graph the functions in Exercise. What symmetries, if any, do the graphs have? Specify the intervals...Problem 38E:

Graph the functions in Exercise. What symmetries, if any, do the graphs have? Specify the intervals...Problem 39E:

Graph the functions in Exercise. What symmetries, if any, do the graphs have? Specify the intervals...Problem 40E:

Graph the functions in Exercise. What symmetries, if any, do the graphs have? Specify the intervals...Problem 41E:

Graph the functions in Exercise. What symmetries, if any, do the graphs have? Specify the intervals...Problem 42E:

Graph the functions in Exercise. What symmetries, if any, do the graphs have? Specify the intervals...Problem 43E:

Graph the functions in Exercise. What symmetries, if any, do the graphs have? Specify the intervals...Problem 44E:

Graph the functions in Exercise. What symmetries, if any, do the graphs have? Specify the intervals...Problem 45E:

Graph the functions in Exercise. What symmetries, if any, do the graphs have? Specify the intervals...Problem 46E:

Graph the functions in Exercise. What symmetries, if any, do the graphs have? Specify the intervals...Problem 47E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 48E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 49E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 50E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 51E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 52E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 53E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 54E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 55E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 56E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 57E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 58E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 59E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 60E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 61E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 62E:

In Exercise 47–62, say whether the function is even, odd, or neither. Given reasons for your...Problem 64E:

Kinetic energy The kinetic energy K of a mass is proportional to the square of its velocity v. If K...Problem 65E:

The variables r and s are inversely proportional, and r = 6 when s = 4. Determine s when r = 10.
Problem 66E:

Boyle’s Law Boyle’s Law says that the volume V of a gas at constant temperature increases whenever...Problem 67E:

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14...Problem 68E:

The accompanying figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse...Problem 69E:

In Exercises 69 and 70, match each equation with its graph. Do not use a graphing device, and give...Problem 70E:

y = 5x
y = 5x
y = x5
Problem 71E:

Graph the functions f(x) = x/2 and g(x) = 1 + (4/x) together to identify the values of x for...Problem 72E:

Graph the functions f(x) = 3/(x − 1) and g(x) = 2/(x + 1) together to identify the values of x for...Problem 73E:

For a curve to be symmetric about the x-axis, the point (x, y) must lie on the curve if and only if...Problem 74E:

Three hundred books sell for $40 each, resulting in a revenue of (300)($40) = $12,000. For each $5...# Browse All Chapters of This Textbook

Chapter 1 - FunctionsChapter 1.1 - Functions And Their GraphsChapter 1.2 - Combining Functions; Shifting And Scaling GraphsChapter 1.3 - Trigonometric FunctionsChapter 1.4 - Graphing With SoftwareChapter 2 - Limits And ContinuityChapter 2.1 - Rates Of Change And Tangent Lines To CurvesChapter 2.2 - Limit Of A Function And Limit LawsChapter 2.3 - The Precise Definition Of A LimitChapter 2.4 - One-sided Limits

Chapter 2.5 - ContinuityChapter 2.6 - Limits Involving Infinity; Asymptotes Of GraphsChapter 3 - DerivativesChapter 3.1 - Tangent Lines And The Derivative At A PointChapter 3.2 - The Derivative As A FunctionChapter 3.3 - Differentiation RulesChapter 3.4 - The Derivative As A Rate Of ChangeChapter 3.5 - Derivatives Of Trigonometric FunctionsChapter 3.6 - The Chain RuleChapter 3.7 - Implicit DifferentiationChapter 3.8 - Related RatesChapter 3.9 - Linearization And DifferentialsChapter 4 - Application Of DerivativesChapter 4.1 - Extreme Values Of Functions On Closed IntervalsChapter 4.2 - The Mean Value TheoremChapter 4.3 - Monotonic Functions And The First Derivative TestChapter 4.4 - Concavity And Curve SketchingChapter 4.5 - Applied OptimizationChapter 4.6 - Newton's MethodChapter 4.7 - AntiderivativesChapter 5 - IntegralsChapter 5.1 - Area And Estimating With Finite SumsChapter 5.2 - Sigma Notation And Limits Of Finite SumsChapter 5.3 - The Definite IntegralChapter 5.4 - The Fundamental Theorem Of CalculusChapter 5.5 - Indefinite Integrals And The Substitution MethodChapter 5.6 - Definite Integral Substitutions And The Area Between CurvesChapter 6 - Applications Of Definite IntegralsChapter 6.1 - Volumes Using Cross-sectionsChapter 6.2 - Volumes Using Cylindrical ShellsChapter 6.3 - Arc LengthChapter 6.4 - Areas Of Surfaces Of RevolutionChapter 6.5 - Work And Fluid ForcesChapter 6.6 - Moments And Centers Of MassChapter 7 - Trascendental FunctionsChapter 7.1 - Inverse Functions And Their DerivativesChapter 7.2 - Natural LogarithmsChapter 7.3 - Exponential FunctionsChapter 7.4 - Exponential Change And Separable Differential EquationsChapter 7.5 - Indeterminate Forms And L'hopital's RuleChapter 7.6 - Inverse Trigonometric FunctionsChapter 7.7 - Hyperbolic FunctionsChapter 7.8 - Relative Rates Of GrowthChapter 8 - Techniques Of IntegrationChapter 8.1 - Using Basic Integration FormulasChapter 8.2 - Integration By PartsChapter 8.3 - Trigonometric IntegralsChapter 8.4 - Trigonometric SubstitutionsChapter 8.5 - Integration Of Rational Functions By Partial FractionsChapter 8.6 - Integral Tables And Computer Algebra SystemsChapter 8.7 - Numerical IntegrationChapter 8.8 - Improper IntegralsChapter 8.9 - ProbabilityChapter 9 - First-order Differential EquationsChapter 9.1 - Solutions, Slope Fields, And Euler's MethodChapter 9.2 - First-order Linear EquationsChapter 9.3 - ApplicationsChapter 9.4 - Graphical Solutions Of Autonomous EquationsChapter 9.5 - Systems Of Equations And Phase PlanesChapter 10 - Infinite Sequences And SeriesChapter 10.1 - SequencesChapter 10.2 - Infinite SeriesChapter 10.3 - The Integral TestChapter 10.4 - Comparison TestsChapter 10.5 - Absolute Convergence; The Ratio And Root TestsChapter 10.6 - Alternating Series And Conditional ConvergenceChapter 10.7 - Power SeriesChapter 10.8 - Taylor And Maclaurin SeriesChapter 10.9 - Convergence Of Taylor SeriesChapter 10.10 - Applications Of Taylor SeriesChapter 11 - Parametric Equations And Polar CoordinatesChapter 11.1 - Parametrizations Of Plane CurvesChapter 11.2 - Calculus With Parametric CurvesChapter 11.3 - Polar CoordinatesChapter 11.4 - Graphing Polar Coordinate EquationsChapter 11.5 - Areas And Lengths In Polar CoordinatesChapter 11.6 - Conic SectionsChapter 11.7 - Conics In Polar CoordinatesChapter 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 - Lines And Planes In SpaceChapter 12.6 - Cylinders And Quadratic SurfacesChapter 13 - Vector-valued Functions And Motion In SpaceChapter 13.1 - Curves In Space And Their TangentsChapter 13.2 - Integrals Of Vector Functions; Projectile MotionChapter 13.3 - Arc Length In SpaceChapter 13.4 - Curvature And Normal Vectors Of A CurveChapter 13.5 - Tangential And Normal Vectors Of A Components Of AccelerationChapter 13.6 - Velocity And Acceleration In Polar CoordinatesChapter 14 - Partial DerivativesChapter 14.1 - Functions Of Several VariablesChapter 14.2 - Limits And Continuity In Higher DimensionsChapter 14.3 - Partial DerivativesChapter 14.4 - The Chain RuleChapter 14.5 - Directional Derivatives And Gradient VectorsChapter 14.6 - Tangent Planes And DifferentialsChapter 14.7 - Extreme Values And Saddle PointsChapter 14.8 - Lagrange MultipliersChapter 14.9 - Taylor's Formula For Two VariablesChapter 14.10 - Partial Derivatives With Constrained VariablesChapter 15 - Multiple IntegralsChapter 15.1 - Double And Iterated Integrals Over RectanglesChapter 15.2 - Double Integrals Over General RegionsChapter 15.3 - Area By Double IntegrationChapter 15.4 - Double Integrals In Polar FormChapter 15.5 - Triple Integrals In Rectangular CoordinatesChapter 15.6 - ApplicationsChapter 15.7 - Triple Integrals In Cylindrical And Spherical CoordinatesChapter 15.8 - Substitution In Multiple IntegralsChapter 16 - Integrals And Vector FieldsChapter 16.1 - Line Integrals Of Scalar FunctionsChapter 16.2 - Vector Fields And Line Integrals: Work, Circulation, And FluxChapter 16.3 - Path Independence, Conservative Fields, And Potential FunctionsChapter 16.4 - Green's Theorem In The PlaneChapter 16.5 - Surfaces And AreaChapter 16.6 - Surface IntegralsChapter 16.7 - Stokes' TheoremChapter 16.8 - The Divergence Theorem And A Unified TheoryChapter 17.1 - Second-order Linear EquationsChapter 17.2 - Nonhomogeneous Linear EquationsChapter 17.3 - ApplicationsChapter 17.4 - Euler EquationsChapter 17.5 - Power-series SolutionsChapter A.1 - Real Numbers And The Real LineChapter A.2 - Mathematical InductionChapter A.3 - Lines, Circles, And ParabolasChapter A.4 - Proofs Of Limit TheoremsChapter A.7 - Complex Numbers

# Sample Solutions for this Textbook

We offer sample solutions for Thomas' Calculus (14th Edition) homework problems. See examples below:

Function: A function is expressed in terms of dependent and independent variable. For every...Given information: The function is g(t). The interval from t=a to t=b. Calculation: Calculate the...Consider a function f is differentiable at a domain value a, then f′(a) is a real number. Then, the...According to the Extreme Value Theorem, If a function f(x) is continuous on a closed interval [a,...To find the area of the shaded region R that lies above the x-axis, below the graph of y=1−x2 and...The volume of a solid of integrable cross-sectional area A(x) from x=a to x=b is the integral of A...If the graph of a function y=f(x) is intersects each horizontal line at most one. Then the function...Write the formula for integration by parts as below. ∫u(x)v′(x)dx=u(x)v(x)−∫v(x)u′(x)dx The...A first-order differential equation is of the form dydx=f(x,y) in which f(x,y) is a function of two...

The infinite sequence of numbers is a function whose domain is the set of positive integers....Description: Parametrization of the curve consists of both equations and intervals of a curve...Description: Generally, the vector is signified by the directed line segment PQ→ with initial point...Description: Rules for differentiating vector functions: Consider, u and v is the differentiable...Suppose D is a set of n-tuples of real numbers (x1, x2,…,xn). A real-valued function f on D is a...The double integral of a function of two variables f(x,y) over a region in the coordinate plane as...Calculation: Definition: If f is defined on a curve C given parametrically by...Formula used: Power Series Method: The power series method for solving a second-order homogenous...

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Thomas' Calculus

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