Solutions for EBK THOMAS' CALCULUS
Problem 5E:
If f(x) = x + 5 and g(x) = x2 − 3, find the...Problem 8E:
In Exercises 7–10, write a formula for .
8.
Problem 9E:
In Exercises 7–10, write a formula for .
9.
Problem 10E:
In Exercises 7–10, write a formula for .
10.
Problem 11E:
Let f(x) = x – 3, , h(x) = x3and j(x) = 2x. Express each of the functions in Exercises 11 and 12 as...Problem 13E:
Copy and complete the following table.
Problem 14E:
Copy and complete the following table.
Problem 15E:
Evaluate each expression using the given table of...Problem 17E:
In Exercises 17 and 18, (a) write formulas for f ∘ g and g ∘ f and find the (b) domain and (c) range...Problem 19E:
19. Let . Find a function y = g(x) so that
Problem 21E:
A balloon’s volume V is given by V = s2 + 2s + 3 cm3, where s is the ambient temperature in °C. The...Problem 23E:
The accompanying figure shows the graph of y = –x2 shifted to two new positions. Write equations for...Problem 24E:
The accompanying figure shows the graph of y = x2 shifted to two new positions. Write equations for...Problem 26E:
The accompanying figure shows the graph of y = –x2 shifted to four new positions. Write an equation...Problem 34E:
Exercises 27–36 tell how many units and in what directions the graphs of the given equations are to...Problem 36E:
Tell how many units and in what directions the graphs of the given equations are to be shifted. Give...Problem 52E:
Graph the functions in Exercises 37–56.
52.
Problem 57E:
The accompanying figure shows the graph of a function f(x) with domain [0, 2] and range [0, 1]. Find...Problem 58E:
The accompanying figure shows the graph of a function g(t) with domain [–4, 0] and range [–3, 0]....Problem 61E:
Vertical and Horizontal Scaling
Exercises 59–68 tell in what direction and by what factor the graphs...Problem 65E:
Tell in what direction and by what factor the graphs of the given functions are to be stretched or...Problem 69E:
Graphing
In Exercises 69–76, graph each function not by plotting points, but by starting with the...Problem 72E:
Graphing
In Exercises 69–76, graph each function not by plotting points, but by starting with the...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
Book Details
For three-semester or four-quarter courses in Calculus for students majoring in mathematics, engineering, or science Clarity and precision Thomas' Calculus helps students reach the level of mathematical proficiency and maturity you require, but with supp
Sample Solutions for this Textbook
We offer sample solutions for EBK THOMAS' CALCULUS 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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