- Chapter 1.1: FUNCTIONS AND CHANGE
- Chapter 1.2: EXPONENTIAL FUNCTIONS
- Chapter 1.3: NEW FUNCTIONS FROM OLD
- Chapter 1.4: LOGARITHMIC FUNCTIONS
- Chapter 1.5: TRIGONOMETRIC FUNCTIONS
- Chapter 1.6: POWERS, POLYNOMIALS, AND RATIONAL FUNCTIONS
- Chapter 1.7: INTRODUCTION TO CONTINUITY
- Chapter 1.8: LIMITS
- Chapter 10.1: TAYLOR POLYNOMIALS
- Chapter 10.2: TAYLOR SERIES
- Chapter 10.3: FINDING AND USING TAYLOR SERIES
- Chapter 10.4: THE ERROR IN TAYLOR POLYNOMIAL APPROXIMATIONS
- Chapter 10.5: FOURIER SERIES
- Chapter 11.1: WHAT IS A DIFFERENTIAL EQUATION?
- Chapter 11.2: SLOPE FIELDS
- Chapter 11.3: EULERS METHOD
- Chapter 11.4: SEPARATION OF VARIABLES
- Chapter 11.5: SEPARATION OF VARIABLES
- Chapter 11.6: APPLICATIONS AND MODELING
- Chapter 11.7: THE LOGISTIC MODEL
- Chapter 11.8: SYSTEMS OF DIFFERENTIAL EQUATIONS
- Chapter 11.9: ANALYZING THE PHASE PLANE
- Chapter 2.1: HOW DO WE MEASURE SPEED?
- Chapter 2.2: THE DERIVATIVE AT A POINT
- Chapter 2.3: THE DERIVATIVE FUNCTION
- Chapter 2.4: INTERPRETATIONS OF THE DERIVATIVE
- Chapter 2.5: THE SECOND DERIVATIVE
- Chapter 2.6: DIFFERENTIABILITY
- Chapter 3.1: POWERS AND POLYNOMIALS
- Chapter 3.10: THEOREMS ABOUT DIFFERENTIABLE FUNCTIONS
- Chapter 3.2: THE EXPONENTIAL FUNCTION
- Chapter 3.3: THE PRODUCT AND QUOTIENT RULES
- Chapter 3.4: THE CHAIN RULE
- Chapter 3.5: THE TRIGONOMETRIC FUNCTIONS
- Chapter 3.6: THE CHAIN RULE AND INVERSE FUNCTIONS
- Chapter 3.7: THE CHAIN RULE AND INVERSE FUNCTIONS
- Chapter 3.8: IMPLICIT FUNCTIONS
- Chapter 3.9: HYPERBOLIC FUNCTIONS
- Chapter 4.1: USING FIRST AND SECOND DERIVATIVES
- Chapter 4.2: OPTIMIZATION
- Chapter 4.3: OPTIMIZATION AND MODELING
- Chapter 4.4: FAMILIES OF FUNCTIONS AND MODELING
- Chapter 4.5: APPLICATIONS TO MARGINALITY
- Chapter 4.6: RATES AND RELATED RATES
- Chapter 4.7: LHOPITALS RULE, GROWTH, AND DOMINANCE
- Chapter 4.8: PARAMETRIC EQUATIONS
- Chapter 5.1: HOW DO WE MEASURE DISTANCE TRAVELED?
- Chapter 5.2: THE DEFINITE INTEGRAL
- Chapter 5.3: THE FUNDAMENTAL THEOREM AND INTERPRETATIONS
- Chapter 5.4: THEOREMS ABOUT DEFINITE INTEGRALS 2
- Chapter 6.1: ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY
- Chapter 6.2: CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY
- Chapter 6.3: DIFFERENTIAL EQUATIONS AND MOTION
- Chapter 6.4: SECOND FUNDAMENTAL THEOREM OF CALCULUS
- Chapter 7.1: INTEGRATION BY SUBSTITUTION
- Chapter 7.2: INTEGRATION BY PARTS
- Chapter 7.3: TABLES OF INTEGRALS
- Chapter 7.4: ALGEBRAIC IDENTITIES AND TRIGONOMETRIC SUBSTITUTIONS
- Chapter 7.5: NUMERICAL METHODS FOR DEFINITE INTEGRALS
- Chapter 7.6: IMPROPER INTEGRALS
- Chapter 7.7: COMPARISON OF IMPROPER INTEGRALS
- Chapter 8.1: AREAS AND VOLUMES
- Chapter 8.2: APPLICATIONS TO GEOMETRY
- Chapter 8.3: AREA AND ARC LENGTH IN POLAR COORDINATES
- Chapter 8.4: DENSITY AND CENTER OF MASS
- Chapter 8.5: APPLICATIONS TO PHYSICS
- Chapter 8.6: APPLICATIONS TO ECONOMICS
- Chapter 8.7: DISTRIBUTION FUNCTIONS
- Chapter 8.8: PROBABILITY, MEAN, AND MEDIAN
- Chapter 9.1: SEQUENCES
- Chapter 9.2: GEOMETRIC SERIES
- Chapter 9.3: CONVERGENCE OF SERIES
- Chapter 9.4: TESTS FOR CONVERGENCE
- Chapter 9.5: POWER SERIES AND INTERVAL OF CONVERGENCE
- Chapter Chapter 1: A LIBRARY OF FUNCTIONS
- Chapter Chapter 10: APPROXIMATING FUNCTIONS USING SERIES
- Chapter Chapter 11: DIFFERENTIAL EQUATIONS
- Chapter Chapter 2: KEY CONCEPT: THE DERIVATIVE
- Chapter Chapter 3: SHORT-CUTS TO DIFFERENTIATION
- Chapter Chapter 4: USING THE DERIVATIVE
- Chapter Chapter 5: KEY CONCEPT: THE DEFINITE INTEGRAL
- Chapter Chapter 6: CONSTRUCTING ANTIDERIVATIVES
- Chapter Chapter 7: INTEGRATION
- Chapter Chapter 8: USING THE DEFINITE INTEGRAL
- Chapter Chapter 9: SEQUENCES AND SERIES
Calculus: Single Variable 6th Edition - Solutions by Chapter
Full solutions for Calculus: Single Variable | 6th Edition
Absolute value of a vector
See Magnitude of a vector.
See Compound fraction.
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers
A fractional expression in which the numerator or denominator may contain fractions
Any solution of the resulting equation that is not a solution of the original equation.
Frequency table (in statistics)
A table showing frequencies.
Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.
y = b.
Line of symmetry
A line over which a graph is the mirror image of itself
A polynomial with exactly one term.
A logarithm with base e.
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.
A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.
Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.
The distance from the center of an ellipse to a point on the ellipse along a line perpendicular to the major axis.
A finite or infinite sum of terms.
Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>
Symmetric property of equality
If a = b, then b = a
A point that lies on both the graph and the x-axis,.