University Calculus3rd EditionUnknown Publisher: PEARSONISBN: 9780134175706
University Calculus
Solutions for University Calculus
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 9E:
Finding Formulas for functions Express the area and perimeter of an equilateral triangle as a...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 f(x)=x. Express the coordinates of...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 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 33E:
For what values of x is
Problem 35E:
Does for all real x? Give reasons for your answer.
Problem 38E:
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 54E:
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 61E:
The variables r and s are inversely proportional, and r = 6 when s = 4. Determine s when r = 10.
Problem 62E:
Boyle’s Law Boyle’s Law says that the volume V of a gas at constant temperature increases whenever...Problem 64E:
The accompanying figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse...Problem 65E:
In Exercises 69 and 70, match each equation with its graph. Do not use a graphing device, and give...Problem 66E:
y = 5x
y = 5x
y = x5
Problem 67E:
Graph the functions f(x) = x/2 and g(x) = 1 + (4/x) together to identify the values of x for...Browse All Chapters of This Textbook
Chapter 1.1 - Functions And Their GraphsChapter 1.2 - Combining Functions; Shifting And Scaling GraphsChapter 1.3 - Trigonometric FunctionsChapter 1.4 - Graphing With SoftwareChapter 1.5 - Exponential FunctionsChapter 1.6 - Inverse Functions And LogarithmsChapter 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 Limit
Chapter 2.4 - One-sided LimitsChapter 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 - Derivatives Of Inverse Functions And LogarithmsChapter 3.9 - Inverse Trigonometric FunctionsChapter 3.10 - Related RatesChapter 3.11 - 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 - Indeterminate Forms And L'hopital's RuleChapter 4.6 - Applied OptimizationChapter 4.7 - Newton's MethodChapter 4.8 - 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 - WorkChapter 6.6 - Moments And Centers Of MassChapter 7 - Integrals And Trascendental FunctionsChapter 7.1 - The Logarithm Defined As An IntegralChapter 7.2 - Exponential Change And Separable Differential EquationsChapter 7.3 - Hyperbolic FunctionsChapter 8 - Techniques Of IntegrationChapter 8.1 - Integration By PartsChapter 8.2 - Trigonometric IntegralsChapter 8.3 - Trigonometric SubstitutionsChapter 8.4 - Integration Of Rational Functions By Partial FractionsChapter 8.5 - Integral Tables And Computer Algebra SystemsChapter 8.6 - Numerical IntegrationChapter 8.7 - Improper IntegralsChapter 9 - Infinite Sequences And SeriesChapter 9.1 - SequencesChapter 9.2 - Infinite SeriesChapter 9.3 - The Integral TestChapter 9.4 - Comparison TestsChapter 9.5 - Absolute Convergence; The Ratio And Root TestsChapter 9.6 - Alternating Series And Conditional ConvergenceChapter 9.7 - Power SeriesChapter 9.8 - Taylor And Maclaurin SeriesChapter 9.9 - Convergence Of Taylor SeriesChapter 9.10 - The Binomial Series And Applications Of Taylor SeriesChapter 10 - Parametric Equations And Polar CoordinatesChapter 10.1 - Parametrizations Of Plane CurvesChapter 10.2 - Calculus With Parametric CurvesChapter 10.3 - Polar CoordinatesChapter 10.4 - Graphing Polar Coordinate EquationsChapter 10.5 - Areas And Lengths In Polar CoordinatesChapter 10.6 - Conics In Polar CoordinatesChapter 11 - Vectors And The Geometry Of SpaceChapter 11.1 - Three-dimensional Coordinate SystemsChapter 11.2 - VectorsChapter 11.3 - The Dot ProductChapter 11.4 - The Cross ProductChapter 11.5 - Lines And Planes In SpaceChapter 11.6 - Cylinders And Quadratic SurfacesChapter 12 - Vector-valued Functions And Motion In SpaceChapter 12.1 - Curves In Space And Their TangentsChapter 12.2 - Integrals Of Vector Functions; Projectile MotionChapter 12.3 - Arc Length In SpaceChapter 12.4 - Curvature And Normal Vectors Of A CurveChapter 12.5 - Tangential And Normal Components Of AccelerationChapter 12.6 - Velocity And Acceleration In Polar CoordinatesChapter 13 - Partial DerivativesChapter 13.1 - Functions Of Several VariablesChapter 13.2 - Limits And Continuity In Higher DimensionsChapter 13.3 - Partial DerivativesChapter 13.4 - The Chain RuleChapter 13.5 - Directional Derivatives And Gradient VectorsChapter 13.6 - Tangent Planes And DifferentialsChapter 13.7 - Extreme Values And Saddle PointsChapter 13.8 - Lagrange MultipliersChapter 14 - Multiple IntegralsChapter 14.1 - Double And Iterated Integrals Over RectanglesChapter 14.2 - Double Integrals Over General RegionsChapter 14.3 - Area By Double IntegrationChapter 14.4 - Double Integrals In Polar FormChapter 14.5 - Triple Integrals In Rectangular CoordinatesChapter 14.6 - Moments And Centers Of MassChapter 14.7 - Triple Integrals In Cylindrical And Spherical CoordinatesChapter 14.8 - Substitution In Multiple IntegralsChapter 15 - Integrals And Vector FieldsChapter 15.1 - Line IntegralsChapter 15.2 - Vector Fields And Line Integrals: Work, Circulation, And FluxChapter 15.3 - Path Independence, Conservative Fields, And Potential FunctionsChapter 15.4 - Green's Theorem In The PlaneChapter 15.5 - Surfaces And AreaChapter 15.6 - Surface IntegralsChapter 15.7 - Stokes' TheoremChapter 15.8 - The Divergence Theorem And A Unified TheoryChapter A.1 - Real Numbers And The Real LineChapter A.2 - Mathematical InductionChapter A.3 - Lines And CirclesChapter A.4 - Conic SectionsChapter A.5 - Proofs Of Limit TheoremsChapter A.8 - Complex Numbers
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Sample Solutions for this Textbook
We offer sample solutions for University Calculus homework problems. See examples below:
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,...Chapter 5, Problem 1GYRThe volume of a solid of integrable cross-sectional area A(x) from x=a to x=b is the integral of A...The natural logarithm is the function given by lnx=∫1x1tdt, x>0. The number e is the number in...Write the formula for integration by parts as below. ∫u(x)v′(x)dx=u(x)v(x)−∫v(x)u′(x)dx The...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...
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