 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: ThreeDimensional 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: SecondOrder Differential Equations
 Chapter 17.1: SecondOrder Linear Equations
 Chapter 17.2: Nonhomogeneous Linear Equations
 Chapter 17.3: Applications of SecondOrder 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: PredatorPrey Systems
Calculus, 5th Edition  Solutions by Chapter
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Calculus,  5th Edition  Solutions by Chapter
Get Full SolutionsThe full stepbystep solution to problem in Calculus, were answered by Patricia, our top Calculus solution expert on 01/25/18, 04:16PM. Calculus, was written by Patricia 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 16503 students have viewed full stepbystep answer.

Arccosine function
See Inverse cosine function.

Average velocity
The change in position divided by the change in time.

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Factored form
The left side of u(v + w) = uv + uw.

Finite series
Sum of a finite number of terms.

Graph of a function ƒ
The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.

Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Minute
Angle measure equal to 1/60 of a degree.

Numerical model
A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Powerreducing identity
A trigonometric identity that reduces the power to which the trigonometric functions are raised.

Radicand
See Radical.

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

RRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the righthand end point of each subinterval.

Solution of an equation or inequality
A value of the variable (or values of the variables) for which the equation or inequality is true

Standard form of a complex number
a + bi, where a and b are real numbers

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Transitive property
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.
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