- Chapter 0: BEFORE CALCULUS
- Chapter 0.1: FUNCTIONS
- Chapter 0.2: NEW FUNCTIONS FROM OLD
- Chapter 0.3: FAMILIES OF FUNCTIONS
- Chapter 0.4: INVERSE FUNCTIONS; INVERSE TRIGONOMETRIC FUNCTIONS
- Chapter 0.5: EXPONENTIAL AND LOGARITHMIC FUNCTIONS
- Chapter 1: LIMITS AND CONTINUITY
- Chapter 1.1: LIMITS (AN INTUITIVE APPROACH)
- Chapter 1.2: COMPUTING LIMITS
- Chapter 1.3: LIMITS AT INFINITY; END BEHAVIOR OF A FUNCTION
- Chapter 1.4: LIMITS (DISCUSSED MORE RIGOROUSLY)
- Chapter 1.5: CONTINUITY
- Chapter 1.6: CONTINUITY OF TRIGONOMETRIC, EXPONENTIAL, AND INVERSE FUNCTIONS
- Chapter 10: PARAMETRIC AND POLAR CURVES; CONIC SECTIONS
- Chapter 10.1: PARAMETRIC EQUATIONS; TANGENT LINES AND ARC LENGTH FOR PARAMETRIC CURVES
- Chapter 10.2: POLAR COORDINATES
- Chapter 10.3: TANGENT LINES, ARC LENGTH, AND AREA FOR POLAR CURVES
- Chapter 10.4: CONIC SECTIONS
- Chapter 10.5: ROTATION OF AXES; SECOND-DEGREE EQUATIONS
- Chapter 10.6: CONIC SECTIONS IN POLAR COORDINATES
- Chapter 11: THREE-DIMENSIONAL SPACE; VECTORS
- Chapter 11.1: RECTANGULAR COORDINATES IN 3-SPACE; SPHERES; CYLINDRICAL SURFACES
- Chapter 11.2: VECTORS
- Chapter 11.3: DOT PRODUCT; PROJECTIONS
- Chapter 11.4: CROSS PRODUCT
- Chapter 11.5: PARAMETRIC EQUATIONS OF LINES
- Chapter 11.6: PLANES IN 3-SPACE
- Chapter 11.7: QUADRIC SURFACES
- Chapter 11.8: CYLINDRICAL AND SPHERICAL COORDINATES
- Chapter 12: VECTOR-VALUED FUNCTIONS
- Chapter 12.1: INTRODUCTION TO VECTOR-VALUED FUNCTIONS
- Chapter 12.2: CALCULUS OF VECTOR-VALUED FUNCTIONS
- Chapter 12.3: CHANGE OF PARAMETER; ARC LENGTH
- Chapter 12.4: UNIT TANGENT, NORMAL, AND BINORMAL VECTORS
- Chapter 12.5: CURVATURE
- Chapter 12.6: MOTION ALONG A CURVE
- Chapter 12.7: KEPLERS LAWS OF PLANETARY MOTION
- Chapter 13: PARTIAL DERIVATIVES
- Chapter 13.1: FUNCTIONS OF TWO OR MORE VARIABLES
- Chapter 13.2: LIMITS AND CONTINUITY
- Chapter 13.3: PARTIAL DERIVATIVES
- Chapter 13.4: DIFFERENTIABILITY, DIFFERENTIALS, AND LOCAL LINEARITY
- Chapter 13.5: THE CHAIN RULE
- Chapter 13.6: DIRECTIONAL DERIVATIVES AND GRADIENTS
- Chapter 13.7: TANGENT PLANES AND NORMAL VECTORS
- Chapter 13.8: MAXIMA AND MINIMA OF FUNCTIONS OF TWO VARIABLES
- Chapter 13.9: LAGRANGE MULTIPLIERS
- Chapter 14: MULTIPLE INTEGRALS 1
- Chapter 14.1: DOUBLE INTEGRALS
- Chapter 14.2: DOUBLE INTEGRALS OVER NONRECTANGULAR REGIONS
- Chapter 14.3: DOUBLE INTEGRALS IN POLAR COORDINATES
- Chapter 14.4: SURFACE AREA; PARAMETRIC SURFACES
- Chapter 14.5: TRIPLE INTEGRALS
- Chapter 14.6: TRIPLE INTEGRALS IN CYLINDRICAL AND SPHERICAL COORDINATES
- Chapter 14.7: CHANGE OF VARIABLES IN MULTIPLE INTEGRALS; JACOBIANS
- Chapter 14.8: CENTERS OF GRAVITY USING MULTIPLE INTEGRALS
- Chapter 15: TOPICS IN VECTOR CALCULUS
- Chapter 15.1: VECTOR FIELDS
- Chapter 15.2: LINE INTEGRALS
- Chapter 15.3: INDEPENDENCE OF PATH; CONSERVATIVE VECTOR FIELDS
- Chapter 15.4: GREENS THEOREM
- Chapter 15.5: SURFACE INTEGRALS
- Chapter 15.6: APPLICATIONS OF SURFACE INTEGRALS; FLUX
- Chapter 15.7: THE DIVERGENCE THEOREM
- Chapter 15.8: STOKES THEOREM
- Chapter 2: THE DERIVATIVE
- Chapter 2.1: TANGENT LINES AND RATES OF CHANGE
- Chapter 2.2: THE DERIVATIVE FUNCTION
- Chapter 2.3: INTRODUCTION TO TECHNIQUES OF DIFFERENTIATION
- Chapter 2.4: THE PRODUCT AND QUOTIENT RULES
- Chapter 2.5: DERIVATIVES OF TRIGONOMETRIC FUNCTIONS
- Chapter 2.6: THE CHAIN RULE
- Chapter 3: TOPICS IN DIFFERENTIATION
- Chapter 3.1: IMPLICIT DIFFERENTIATION
- Chapter 3.2: DERIVATIVES OF LOGARITHMIC FUNCTIONS
- Chapter 3.3: DERIVATIVES OF EXPONENTIAL AND INVERSE TRIGONOMETRIC FUNCTIONS
- Chapter 3.4: RELATED RATES
- Chapter 3.5: LOCAL LINEAR APPROXIMATION; DIFFERENTIALS
- Chapter 3.6: LHPITALS RULE; INDETERMINATE FORMS
- Chapter 4: THE DERIVATIVE IN GRAPHING AND APPLICATIONS
- Chapter 4.1: ANALYSIS OF FUNCTIONS I: INCREASE, DECREASE, AND CONCAVITY
- Chapter 4.2: ANALYSIS OF FUNCTIONS II: RELATIVE EXTREMA; GRAPHING POLYNOMIALS
- Chapter 4.3: ANALYSIS OF FUNCTIONS III: RATIONAL FUNCTIONS, CUSPS, AND VERTICAL TANGENTS
- Chapter 4.4: ABSOLUTE MAXIMA AND MINIMA
- Chapter 4.5: APPLIED MAXIMUM AND MIMIMUM PROBLEMS
- Chapter 4.6: RECTILINEAR MOTION
- Chapter 4.7: NEWTONS METHOD
- Chapter 4.8: ROLLES THEOREM; MEAN-VALUE THEOREM
- Chapter 5: INTEGRATION
- Chapter 5.1: AN OVERVIEW OF THE AREA PROBLEM
- Chapter 5.2: THE INDEFINITE INTEGRAL
- Chapter 5.3: INTEGRATION BY SUBSTITUTION
- Chapter 5.4: THE DEFINITION OF AREA AS A LIMIT; SIGMA NOTATION
- Chapter 5.5: THE DEFINITE INTEGRAL
- Chapter 5.6: THE FUNDAMENTAL THEOREM OF CALCULUS
- Chapter 5.7: RECTILINEAR MOTION REVISITED USING INTEGRATION
- Chapter 5.8: AVERAGE VALUE OF A FUNCTION AND ITS APPLICATIONS
- Chapter 5.9: EVALUATING DEFINITE INTEGRALS BY SUBSTITUTION
- Chapter 6: APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING
- Chapter 6.1: AREA BETWEEN TWO CURVES
- Chapter 6.2: VOLUMES BY SLICING; DISKS AND WASHERS
- Chapter 6.3: VOLUMES BY CYLINDRICAL SHELLS
- Chapter 6.4: LENGTH OF A PLANE CURVE
- Chapter 6.5: AREA OF A SURFACE OF REVOLUTION
- Chapter 6.6: WORK
- Chapter 6.7: MOMENTS, CENTERS OF GRAVITY, AND CENTROIDS
- Chapter 6.8: MOMENTS, CENTERS OF GRAVITY, AND CENTROIDS
- Chapter 6.9: HYPERBOLIC FUNCTIONS AND HANGING CABLES
- Chapter 7: PRINCIPLES OF INTEGRAL EVALUATION
- Chapter 7.1: AN OVERVIEW OF INTEGRATION METHODS
- Chapter 7.2: INTEGRATION BY PARTS
- Chapter 7.3: INTEGRATING TRIGONOMETRIC FUNCTIONS
- Chapter 7.4: TRIGONOMETRIC SUBSTITUTIONS
- Chapter 7.5: INTEGRATING RATIONAL FUNCTIONS BY PARTIAL FRACTIONS
- Chapter 7.6: USING COMPUTER ALGEBRA SYSTEMS AND TABLES OF INTEGRALS
- Chapter 7.7: NUMERICAL INTEGRATION; SIMPSONS RULE
- Chapter 7.8: IMPROPER INTEGRALS
- Chapter 8: MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
- Chapter 8.1: MODELING WITH DIFFERENTIAL EQUATIONS
- Chapter 8.2: SEPARATION OF VARIABLES
- Chapter 8.3: SLOPE FIELDS; EULERS METHOD
- Chapter 8.4: FIRST-ORDER DIFFERENTIAL EQUATIONS AND APPLICATIONS
- Chapter 9: INFINITE SERIES
- Chapter 9.1: SEQUENCES
- Chapter 9.10: DIFFERENTIATING AND INTEGRATING POWER SERIES; MODELING WITH TAYLOR SERIES
- Chapter 9.2: MONOTONE SEQUENCES
- Chapter 9.3: INFINITE SERIES
- Chapter 9.4: CONVERGENCE TESTS
- Chapter 9.5: THE COMPARISON, RATIO, AND ROOT TESTS
- Chapter 9.6: ALTERNATING SERIES; ABSOLUTE AND CONDITIONAL CONVERGENCE
- Chapter 9.7: MACLAURIN AND TAYLOR POLYNOMIALS
- Chapter 9.8: MACLAURIN AND TAYLOR SERIES; POWER SERIES
- Chapter 9.9: CONVERGENCE OF TAYLOR SERIES
Calculus: Early Transcendentals, 10th Edition - Solutions by Chapter
Full solutions for Calculus: Early Transcendentals, | 10th Edition
ISBN: 9780470647691
Solutions by Chapter
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Key Calculus Terms and definitions covered in this textbook
-
Addition principle of probability.
P(A or B) = P(A) + P(B) - P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)
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Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots
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Arcsecant function
See Inverse secant function.
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Common difference
See Arithmetic sequence.
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Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.
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Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.
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Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.
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Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a - ƒ(x) = q.
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Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.
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Nautical mile
Length of 1 minute of arc along the Earth’s equator.
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Parameter interval
See Parametric equations.
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Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.
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Principle of mathematical induction
A principle related to mathematical induction.
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Product of functions
(ƒg)(x) = ƒ(x)g(x)
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Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.
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RRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the right-hand end point of each subinterval.
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Subtraction
a - b = a + (-b)
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Time plot
A line graph in which time is measured on the horizontal axis.
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Tree diagram
A visualization of the Multiplication Principle of Probability.
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y-axis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.