- Chapter 1: REVIEW PROBLEMS FOR CHAPTER ONE
- Chapter 1.1: WHAT IS A FUNCTION?
- Chapter 1.10: PERIODIC FUNCTIONS
- Chapter 1.2: LINEAR FUNCTIONS
- Chapter 1.3: AVERAGE RATE OF CHANGE AND RELATIVE CHANGE
- Chapter 1.4: APPLICATIONS OF FUNCTIONS TO ECONOMICS
- Chapter 1.5: EXPONENTIAL FUNCTIONS
- Chapter 1.6: THE NATURAL LOGARITHM
- Chapter 1.7: EXPONENTIAL GROWTH AND DECAY
- Chapter 1.8: NEW FUNCTIONS FROM OLD
- Chapter 1.9: PROPORTIONALITY AND POWER FUNCTIONS
- Chapter 10: REVIEW PROBLEMS FOR CHAPTER TEN
- Chapter 10.1: GEOMETRIC SERIES
- Chapter 10.2: APPLICATIONS TO BUSINESS AND ECONOMICS
- Chapter 10.3: APPLICATIONS TO THE NATURAL SCIENCES
- Chapter 2: REVIEW PROBLEMS FOR CHAPTER TWO
- Chapter 2.1: INSTANTANEOUS RATE OF CHANGE
- Chapter 2.2: THE DERIVATIVE FUNCTION
- Chapter 2.3: INTERPRETATIONS OF THE DERIVATIVE
- Chapter 2.4: THE SECOND DERIVATIVE
- Chapter 2.5: MARGINAL COST AND REVENUE
- Chapter 3: REVIEW PROBLEMS FOR CHAPTER THREE
- Chapter 3.1: DERIVATIVE FORMULAS FOR POWERS AND POLYNOMIALS
- Chapter 3.2: EXPONENTIAL AND LOGARITHMIC FUNCTIONS
- Chapter 3.3: THE CHAIN RULE
- Chapter 3.4: THE PRODUCT AND QUOTIENT RULES
- Chapter 3.5: DERIVATIVES OF PERIODIC FUNCTIONS
- Chapter 4: REVIEW PROBLEMS FOR CHAPTER FOUR
- Chapter 4.1: LOCAL MAXIMA AND MINIMA
- Chapter 4.2: INFLECTION POINTS
- Chapter 4.3: GLOBAL MAXIMA AND MINIMA
- Chapter 4.4: PROFIT, COST, AND REVENUE
- Chapter 4.5: AVERAGE COST
- Chapter 4.6: ELASTICITY OF DEMAND
- Chapter 4.7: LOGISTIC GROWTH
- Chapter 4.8: THE SURGE FUNCTION AND DRUG CONCENTRATION
- Chapter 5: REVIEW PROBLEMS FOR CHAPTER FIVE
- Chapter 5.1: DISTANCE AND ACCUMULATED CHANGE
- Chapter 5.2: THE DEFINITE INTEGRAL
- Chapter 5.3: THE DEFINITE INTEGRAL AS AREA
- Chapter 5.4: INTERPRETATIONS OF THE DEFINITE INTEGRAL
- Chapter 5.5: TOTAL CHANGE AND THE FUNDAMENTAL THEOREM OF CALCULUS
- Chapter 5.6: AVERAGE VALUE
- Chapter 6: REVIEW PROBLEMS FOR CHAPTER SIX
- Chapter 6.1: ANALYZING ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY
- Chapter 6.2: ANTIDERIVATIVES AND THE INDEFINITE INTEGRAL
- Chapter 6.3: USING THE FUNDAMENTAL THEOREM TO FIND DEFINITE INTEGRALS
- Chapter 6.4: APPLICATION: CONSUMER AND PRODUCER SURPLUS
- Chapter 6.5: APPLICATION: PRESENT AND FUTURE VALUE
- Chapter 6.6: INTEGRATION BY SUBSTITUTION
- Chapter 6.7: INTEGRATION BY PARTS
- Chapter 7: REVIEW PROBLEMS FOR CHAPTER SEVEN
- Chapter 7.1: DENSITY FUNCTIONS
- Chapter 7.2: CUMULATIVE DISTRIBUTION FUNCTIONS AND PROBABILITY
- Chapter 7.3: THE MEDIAN AND THE MEAN
- Chapter 8: REVIEW PROBLEMS FOR CHAPTER EIGHT
- Chapter 8.1: UNDERSTANDING FUNCTIONS OF TWO VARIABLES
- Chapter 8.2: CONTOUR DIAGRAMS
- Chapter 8.3: PARTIAL DERIVATIVES
- Chapter 8.4: COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY
- Chapter 8.5: CRITICAL POINTS AND OPTIMIZATION
- Chapter 8.6: CONSTRAINED OPTIMIZATION
- Chapter 9: REVIEW PROBLEMS FOR CHAPTER NINE
- Chapter 9.1: MATHEMATICAL MODELING: SETTING UP A DIFFERENTIAL EQUATION
- Chapter 9.2: SOLUTIONS OF DIFFERENTIAL EQUATIONS
- Chapter 9.3: SLOPE FIELDS
- Chapter 9.4: EXPONENTIAL GROWTH AND DECAY
- Chapter 9.5: APPLICATIONS AND MODELING
- Chapter 9.6: MODELING THE INTERACTION OF TWO POPULATIONS
- Chapter 9.7: MODELING THE SPREAD OF A DISEASE
- Chapter Appendix A: Problems for Appendix A
- Chapter Appendix B: Problems for Appendix B
Applied Calculus 5th Edition - Solutions by Chapter
Full solutions for Applied Calculus | 5th Edition
See Inverse secant function.
An observational study that gathers data from an entire population
Complex numbers a + bi and a - bi
An identity involving a trigonometric function of 2u
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).
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.
Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + ae-kx, where a, b, c, and k are positive with b < 1. c is the limit to growth
The value of |r| at the point on the graph of a polar equation that has the maximum distance from the pole
Two lines that are both vertical or have equal slopes.
Numbers that can be written as a/b, where a and b are integers, and b ? 0.
Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.
Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.
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.
Solution of an equation or inequality
A value of the variable (or values of the variables) for which the equation or inequality is true
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.
A special form for a system of linear equations that facilitates finding the solution.
A point that lies on both the graph and the y-axis.
Zero of a function
A value in the domain of a function that makes the function value zero.
The vector <0,0> or <0,0,0>.
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