- Chapter 1: Functions and Models
- Chapter 1.1: Four Ways to Represent a Function
- Chapter 1.2: Mathematical Models: A Catalog of Essential Functions
- Chapter 1.3: New Functions from Old Functions
- Chapter 1.4: Graphing Calculators and Computers
- Chapter 1.5: Exponential Functions
- Chapter 1.6: Inverse Functions and Logarithms
- Chapter 10: Parametric Equations and Polar Coordinates
- Chapter 10.1: Curves Defined by Parametric Equations
- Chapter 10.2: Calculus with Parametric Curves
- Chapter 10.3: Polar Coordinates
- Chapter 10.4: Areas and Lengths in Polar Coordinates
- Chapter 10.5: Conic Sections
- Chapter 10.6: Conic Sections in Polar Coordinates
- Chapter 11: Infinite Sequences and Series
- Chapter 11.1: Sequences
- Chapter 11.10: Taylor and Maclaurin Series
- Chapter 11.11: The Binomial Series
- Chapter 11.12: Applications of Taylor Polynomials
- Chapter 11.2: Series
- Chapter 11.3: The Integral Test and Estimates of Sums
- Chapter 11.4: The Comparison Tests
- Chapter 11.5: Alternating Series
- Chapter 11.6: Absolute Convergence and the Ratio and Root Tests
- Chapter 11.7: Strategy for Testing Series
- Chapter 11.8: Power Series
- Chapter 11.9: Representations of Functions as Power Series
- Chapter 12: Vectors and the Geometry of Space
- Chapter 12.1: Three-Dimensional Coordinate Systems
- Chapter 12.2: Vectors
- Chapter 12.3: The Dot Product
- Chapter 12.4: The Cross Product
- Chapter 12.5: Equations of Lines and Planes
- Chapter 12.6: Cylinders and Quadric Surfaces
- Chapter 12.7: Cylindrical and Spherical Coordinates
- Chapter 13: Vector Functions
- Chapter 13.1: Vector Functions and Space Curves
- Chapter 13.2: Derivatives and Integrals of Vector Functions
- Chapter 13.3: Arc Length and Curvature
- Chapter 13.4: Motion in Space: Velocity and Acceleration
- Chapter 14: Partial Derivatives
- Chapter 14.1: Functions of Several Variables
- Chapter 14.2: Limits and Continuity
- Chapter 14.3: Partial Derivatives
- Chapter 14.4: Tangent Planes and Linear Approximations
- Chapter 14.5: The Chain Rule
- Chapter 14.6: Directional Derivatives and the Gradient Vector
- Chapter 14.7: Maximum and Minimum Values
- Chapter 14.8: Lagrange Multipliers
- Chapter 15: Multiple Integrals
- Chapter 15.1: Double Integrals over Rectangles
- Chapter 15.2: Iterated Integrals
- Chapter 15.3: Double Integrals over General Regions
- Chapter 15.4: Double Integrals in Polar Coordinates
- Chapter 15.5: Applications of Double Integrals
- Chapter 15.6: Surface Area
- Chapter 15.7: Triple Integrals
- Chapter 15.8: Triple Integrals in Cylindrical and Spherical Coordinates
- Chapter 15.9: Change of Variables in Multiple Integrals
- Chapter 16: Vector Calculus
- Chapter 16.1: Vector Fields
- Chapter 16.2: Line Integrals
- Chapter 16.3: The Fundamental Theorem for Line Integrals
- Chapter 16.4: The Fundamental Theorem for Line Integrals
- Chapter 16.5: Curl and Divergence
- Chapter 16.6: Parametric Surfaces and Their Areas
- Chapter 16.7: Surface Integrals
- Chapter 16.8: Stokes Theorem
- Chapter 16.9: The Divergence Theorem
- Chapter 17: Second-Order Differential Equations
- Chapter 17.1: Second-Order Linear Equations
- Chapter 17.2: Nonhomogeneous Linear Equations
- Chapter 17.3: Applications of Second-Order Differential Equations
- Chapter 17.4: Series Solutions
- Chapter 2: Limits and Derivatives
- Chapter 2.1: The Tangent and Velocity Problems
- Chapter 2.2: The Limit of a Function
- Chapter 2.3: Calculating Limits Using the Limit Laws
- Chapter 2.4: The Precise Definition of a Limit
- Chapter 2.5: Continuity
- Chapter 2.6: Limits at Infinity; Horizontal Asymptotes
- Chapter 2.7: Tangents, Velocities, and Other Rates of Change
- Chapter 2.8: Derivatives
- Chapter 2.9: The Derivative as a Function
- Chapter 3: Differentiation Rules
- Chapter 3.1: Derivatives of Polynomials and Exponential Functions
- Chapter 3.10: Related Rates
- Chapter 3.11: Linear Approximations and Differentials
- Chapter 3.3: -
- Chapter 3.4: Derivatives of Trigonometric Functions
- Chapter 3.5: The Chain Rule
- Chapter 3.6: Implicit Differentiation
- Chapter 3.7: Higher Derivatives
- Chapter 3.8: Derivatives of Logarithmic Functions
- Chapter 3.9: Hyperbolic Functions
- Chapter 4: Applications of Differentiation
- Chapter 4.1: Maximum and Minimum Values
- Chapter 4.10: Antiderivatives
- Chapter 4.2: The Mean Value Theorem
- Chapter 4.3: How Derivatives Affect the Shape of a Graph
- Chapter 4.4: Indeterminate Forms and LHospitals Rule
- Chapter 4.5: Summary of Curve Sketching
- Chapter 4.6: Graphing with Calculus and Calculators
- Chapter 4.7: Optimization Problems
- Chapter 4.8: Applications to Business and Economics
- Chapter 4.9: Newtons Method
- Chapter 5: Integrals
- Chapter 5.1: Areas and Distances
- Chapter 5.2: The Definite Integral
- Chapter 5.3: The Fundamental Theorem of Calculus
- Chapter 5.4: Indefinite Integrals and the Net Change Theorem
- Chapter 5.5: The Substitution Rule
- Chapter 5.6: The Logarithm Defined as an Integral
- Chapter 6: Applications of Integration
- Chapter 6.1: Areas between Curves
- Chapter 6.2: Volumes
- Chapter 6.3: Volumes by Cylindrical Shells
- Chapter 6.4: Work
- Chapter 6.5: Average Value of a Function
- Chapter 7: Techniques of Integration
- Chapter 7.1: Integration by Parts
- Chapter 7.2: Trigonometric Integrals
- Chapter 7.3: Trigonometric Substitution
- Chapter 7.4: Integration of Rational Functions by Partial Fractions
- Chapter 7.5: Strategy for Integration
- Chapter 7.6: Integration Using Tables and Computer Algebra Systems
- Chapter 7.7: Approximate Integration
- Chapter 7.8: Improper Integrals
- Chapter 8: Further Applications of Integration
- Chapter 8.1: Arc Length
- Chapter 8.2: Area of a Surface of Revolution
- Chapter 8.3: Applications to Physics and Engineering
- Chapter 8.4: Applications to Economics and Biology
- Chapter 8.5: Probability
- Chapter 9: Differential Equations
- Chapter 9.1: Modeling with Differential Equations
- Chapter 9.2: Direction Fields and Eulers Method
- Chapter 9.3: Separable Equations
- Chapter 9.4: Exponential Growth and Decay
- Chapter 9.5: The Logistic Equation
- Chapter 9.6: Linear Equations
- Chapter 9.7: Predator-Prey Systems
Calculus, 5th Edition - Solutions by Chapter
Full solutions for Calculus, | 5th Edition
ISBN: 9780534393397
Solutions by Chapter
The full step-by-step solution to problem in Calculus, were answered by , our top Calculus solution expert on 01/25/18, 04:16PM. Calculus, was written by and is associated to the ISBN: 9780534393397. This expansive textbook survival guide covers the following chapters: 142. This textbook survival guide was created for the textbook: Calculus,, edition: 5. Since problems from 142 chapters in Calculus, have been answered, more than 40884 students have viewed full step-by-step answer.
Key Calculus Terms and definitions covered in this textbook
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Arctangent function
See Inverse tangent function.
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Complex fraction
See Compound fraction.
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Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x) - ƒ(a) x - a provided the limit exists
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Dihedral angle
An angle formed by two intersecting planes,
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Dot product
The number found when the corresponding components of two vectors are multiplied and then summed
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Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse
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Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)
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Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012 - ƒ1a - 0.00120.002
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Opposite
See Additive inverse of a real number and Additive inverse of a complex number.
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Phase shift
See Sinusoid.
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Positive numbers
Real numbers shown to the right of the origin on a number line.
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Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.
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Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.
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Repeated zeros
Zeros of multiplicity ? 2 (see Multiplicity).
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Speed
The magnitude of the velocity vector, given by distance/time.
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Terminal side of an angle
See Angle.
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Third quartile
See Quartile.
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Variable
A letter that represents an unspecified number.
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Vertical component
See Component form of a vector.
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Zero of a function
A value in the domain of a function that makes the function value zero.