Solutions for Calculus: Single And Multivariable, 7e Wileyplus Registration Card + Loose-leaf Print Companion
Problem 1RE:
Find formulas for the functions described in Exercises 18. A line with slope 2 and x-intercept 5.Problem 2RE:
Find formulas for the functions described in Exercises 18. A parabola opening downward with its...Problem 3RE:
Find formulas for the functions described in Exercises 18. A parabola with x-intercepts 1 and...Problem 4RE:
Find formulas for the functions described in Exercises 18. The bottom half of a circle centered at...Problem 5RE:
Find formulas for the functions described in Exercises 18. The top half of a circle with center (1,...Problem 6RE:
Find formulas for the functions described in Exercises 18. A cubic polynomial having x-intercepts at...Problem 7RE:
Find formulas for the functions described in Exercises 18. A rational function of the form y = ax/(x...Problem 8RE:
Find formulas for the functions described in Exercises 18. A cosine curve with a maximum at (0, 5),...Problem 9RE:
Find derivatives for the functions in Exercises 1-73. Assume a, b, c, and k are constants. 9....Problem 11RE:
The entire graph of f(x) is shown in Figure 1.1. a) What is the domain of f(x)? b) What is the range...Problem 12RE:
For f(n) = 3n2 2 and g(n) = n +1, find and simplify: a) f(n) + g(n) b) f(n)g(n) c) The domain of...Problem 13RE:
Let m = f(A) be the minimum annual gross income, in thousands of dollars, needed to obtain a 30-year...Problem 14RE:
For Exercises 1417, solve for t using logs. 5t = 7Problem 15RE:
For Exercises 1417, solve for t using logs. 2 = (1.02)tProblem 16RE:
For Exercises 1417, solve for t using logs. 7 3t = 5 2tProblem 20RE:
For Exercises 2021, find functions f and g such that h(x) = f(g(x)). [Note: Do not choose f(x) = x...Problem 21RE:
For Exercises 2021, find functions f and g such that h(x) = f(g(x)). [Note: Do not choose f(x) = x...Problem 24RE:
Consider the function y = 5 + cos(3x). (a) What is its amplitude? (b) What is its period? (c) Sketch...Problem 25RE:
Determine the end behavior of each function as x + and as x . (a) f(x)=x7 (b) f(x)=3x+7x312x4 (c)...Problem 28RE:
Find possible formulas for the graphs in Exercises 2841.Problem 29RE:
Find possible formulas for the graphs in Exercises 2841.Problem 30RE:
Find possible formulas for the graphs in Exercises 2841.Problem 31RE:
Find possible formulas for the graphs in Exercises 2841.Problem 32RE:
Find possible formulas for the graphs in Exercises 2841.Problem 33RE:
Find possible formulas for the graphs in Exercises 2841.Problem 34RE:
Find possible formulas for the graphs in Exercises 2841.Problem 35RE:
Find possible formulas for the graphs in Exercises 2841.Problem 36RE:
Find possible formulas for the graphs in Exercises 2841.Problem 37RE:
Find possible formulas for the graphs in Exercises 2841.Problem 38RE:
Find possible formulas for the graphs in Exercises 2841.Problem 39RE:
Find possible formulas for the graphs in Exercises 2841.Problem 40RE:
Find possible formulas for the graphs in Exercises 2841.Problem 41RE:
Find possible formulas for the graphs in Exercises 2841.Problem 44RE:
Use Figure 1.2 to estimate the limits if they exist: (a) limx0f(x) (b) (b) limx1f(x) (c) limx2f(x)...Problem 45RE:
For the functions in Exercises 4546, use algebra to evaluate the limits limxa+f(x), limxaf(x), and...Problem 46RE:
For the functions in Exercises 4546, use algebra to evaluate the limits limxa+f(x), limxaf(x), and...Problem 47RE:
Use the graph of g(t) in Figure 1.3 to give approximate values for the following limits (if they...Problem 48RE:
Use Figure 1.4 to give approximate values for the following limits (if they exist). (a) limx2f(x)...Problem 53RE:
Use a graph to estimate each of the limits in Exercises 5356. Use radians unless degrees are...Problem 54RE:
Use a graph to estimate each of the limits in Exercises 5356. Use radians unless degrees are...Problem 55RE:
Use a graph to estimate each of the limits in Exercises 5356. Use radians unless degrees are...Problem 56RE:
Use a graph to estimate each of the limits in Exercises 5356. Use radians unless degrees are...Problem 57RE:
In Exercises 5758, (a) Make a table of values of f(x) for x = 0.9, 0.99, 1.01, and 1.1. (b) Use the...Problem 58RE:
In Exercises 5758, (a) Make a table of values of f(x) for x = 0.9, 0.99, 1.01, and 1.1. (b) Use the...Problem 59RE:
For Exercises 5961, use the end behavior of the denominator and numerator to find the limit as x ....Problem 60RE:
For Exercises 5961, use the end behavior of the denominator and numerator to find the limit as x ....Problem 61RE:
For Exercises 5961, use the end behavior of the denominator and numerator to find the limit as x ....Problem 73RE:
The yield, Y, of an apple orchard (in bushels) as a function of the amount, a, of fertilizer (in...Problem 74RE:
The graph of Fahrenheit temperature, F, as a function of Celsius temperature, C, is a line. You know...Problem 75RE:
The demand function for a certain product, q = D(p), is linear, where p is the price per item in...Problem 76RE:
A flight from Dulles Airport in Washington, DC, to La-Guardia Airport in New York City has to circle...Problem 77RE:
The force, F, between two atoms depends on the distance r separating them. See Figure 1.6. A...Problem 78RE:
When the Olympic Games were held outside Mexico City in 1968, there was much discussion about the...Problem 79RE:
The population of the Ukraine fell from 46.01 million in 2010 to 45.43 million in 2014.1 Assuming...Problem 80RE:
During April 2006, Zimbabwes inflation rate averaged 0.67% a day. This means that, on average,...Problem 82RE:
A kilogram weighs about 2.2 pounds. (a) Write a formula for the function, f, which gives an objects...Problem 83RE:
The graph of f(x) is a parabola that opens upward and the graph of g(x) is a line with negative...Problem 84RE:
Each of the functions in the table is increasing over its domain, but each increases in a different...Problem 85RE:
A culture of 100 bacteria doubles after 2 hours. How long will it take for the number of bacteria to...Problem 86RE:
If f(x) = a ln(x + 2), how does increasing a affect (a) The y-intercept? (b) The x-intercept?Problem 89RE:
The air in a factory is being filtered so that the quantity of a pollutant, P (in mg/liter), is...Problem 90RE:
The half-life of radioactive strontium-90 is 29 years. In 1960, radioactive strontium-90 was...Problem 92RE:
In an electrical outlet, the voltage, V, in volts, is given as a function of time, t, in seconds, by...Problem 93RE:
In a US household, the voltage in volts in an electric outlet is given by V=156sin(120t), where t is...Problem 94RE:
(a) How does the parameter A affect the graph of y = A sin(Bx)? (Plot for A = 1, 2, 3 with B = 1.)...Problem 95RE:
Water is flowing down a cylindrical pipe of radius r. (a) Write a formula for the volume, V, of...Problem 96RE:
Values of three functions are given in Table 1.1, rounded to two decimal places. Two are power...Problem 97RE:
Figure 1.8 shows the hat function hN(x)={0ifxN11+xNifN1xN1+NxifNxN+10ifN+1x. (a) Graph the function...Problem 98RE:
The point P moves around the circle of radius 5 shown in Figure 1.9. The angle , in radians, is...Problem 99RE:
Match the following functions with the graphs in Figure 1.11. Assume 0 b a. (a) y=axx (b)...Problem 100RE:
Use a computer or calculator to sketch the functions y(x) = sin x and zk(x) = kx for k =...Problem 101RE:
If possible, choose k so that the following function is continuous on any interval:...Problem 102RE:
Find k so that the following function is continuous on any interval: j(x)={kcosxx0exkx0Problem 103RE:
A car is coasting down a hill at a constant speed. A truck collides with the rear of the car,...Problem 104RE:
By graphing y = 3 2et estimate the limit limt(32et). Use the properties of limits and the fact that...Problem 106RE:
(a) For k = 1, sketch f(x)={kx0x2(x2)2+32x4. (b) Find the value of k so that f(x) is continuous at x...Problem 107RE:
(a) Graph a continuous function g with all the following properties: (i) g(2) = 5 (ii) g(x) has a...Problem 108RE:
In Problems 108111, let g(t) be a function whose graph has a vertical asymptote at t = 5 and...Problem 109RE:
In Problems 108111, let g(t) be a function whose graph has a vertical asymptote at t = 5 and...Problem 110RE:
In Problems 108111, let g(t) be a function whose graph has a vertical asymptote at t = 5 and...Problem 111RE:
In Problems 108111, let g(t) be a function whose graph has a vertical asymptote at t = 5 and...Problem 112RE:
In Problems 112113, use the given value of f(5) and the values of f(x) in the table. (a) Assuming it...Problem 113RE:
In Problems 112113, use the given value of f(5) and the values of f(x) in the table. (a) Assuming it...Problem 114RE:
In Problems 114116, find the limits. limh01/(x+h)21/x2hProblem 115RE:
In Problems 114116, find the limits. limh0x+hxhProblem 117RE:
For Problems 117120, if possible, calculate the limits using the properties of limits. Justify each...Problem 118RE:
For Problems 117120, if possible, calculate the limits using the properties of limits. Justify each...Problem 119RE:
For Problems 117120, if possible, calculate the limits using the properties of limits. Justify each...Problem 120RE:
For problems 117-120, if possible, calculate the limits using the properties of limits. Justify each...Problem 121RE:
For Problems 121124, evaluate the limit, using the rules for limits together with limxax=a and...Problem 122RE:
For Problems 121124, evaluate the limit, using the rules for limits together with limxax=a and...Problem 123RE:
For Problems 121124, evaluate the limit, using the rules for limits together with limxax=a and...Problem 124RE:
For Problems 121124, evaluate the limit, using the rules for limits together with limxax=a and...Problem 125RE:
The notation limx0+ means that we only consider values of x greater than 0. Estimate the limit...Problem 126RE:
Let limxf(x)= and limxg(x)=. Give possible formulas for f(x) and g(x) if (a) limxf(x)+g(x)= (b)...Problem 127RE:
(a) Evaluate the limit limx0(x1x). (b) Explain why you cannot use Property 3 of the limit properties...Problem 128RE:
For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =...Problem 129RE:
For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =...Problem 130RE:
For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =...Problem 131RE:
For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =...Problem 132RE:
For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =...Problem 133RE:
For the functions in Problems 128135, do the following: (a) Make a table of values of f(x) for x =...Browse All Chapters of This Textbook
Chapter 1 - Foundation For Calculus: Functions And LimitsChapter 1.1 - Functions And ChangeChapter 1.2 - Exponential FunctionsChapter 1.3 - New Functions From OldChapter 1.4 - Logarithmic FunctionsChapter 1.5 - Trigonometric FunctionsChapter 1.6 - Powers, Polynomials, And Rational FunctionsChapter 1.7 - Introduction To Limits And ContinuityChapter 1.8 - Extending The Idea Of A LimitChapter 1.9 - Further Limit Calculations Using Algebra
Chapter 1.10 - Optional Preview Of The Formal Definition Of A LimitChapter 2 - Key Concept: The DerivativeChapter 2.1 - How Do We Measure Speed?Chapter 2.2 - The Derivative At A PointChapter 2.3 - The Derivative FunctionChapter 2.4 - Interpretations Of The DerivativeChapter 2.5 - The Second DerivativeChapter 2.6 - DifferentiabilityChapter 3 - Short-cuts To DifferentiationChapter 3.1 - Powers And PolynomialsChapter 3.2 - The Exponential FunctionChapter 3.3 - The Product And Quotient RulesChapter 3.4 - The Chain RuleChapter 3.5 - The Trigonometric FunctionsChapter 3.6 - The Chain Rule And Inverse FunctionsChapter 3.7 - Implicit FunctionsChapter 3.8 - Hyperbolic FunctionsChapter 3.9 - Linear Approximation And The DerivativeChapter 3.10 - Theorems About Differentiable FunctionsChapter 4 - Using The DerivativeChapter 4.1 - Using First And Second DerivativesChapter 4.2 - OptimizationChapter 4.3 - Optimization And ModelingChapter 4.4 - Families Of Functions And ModelingChapter 4.5 - Applications To MarginalityChapter 4.6 - Rates And Related RatesChapter 4.7 - L’hopital’s Rule, Growth, And DominanceChapter 4.8 - Parametric EquationsChapter 5.1 - How Do We Measure Distance Traveled?Chapter 8.1 - Areas And VolumesChapter 10.2 - Taylor SeriesChapter 10.3 - Finding And Using Taylor SeriesChapter 13.2 - Vectors In GeneralChapter 14.1 - The Partial DerivativeChapter 14.2 - Computing Partial Derivatives AlgebraicallyChapter 14.3 - Local Linearity And The DifferentialChapter 14.4 - Gradients And Directional Derivatives In The PlaneChapter 18.1 - The Idea Of A Line IntegralChapter 20.1 - The Curl Of A Vector FieldChapter 21 - Parameters, Coordinates, And Integrals
Book Details
Calculus: Single and Multivariable, 7th Edition continues the effort to promote courses in which understanding and computation reinforce each other. The 7th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secondary schools. This new edition has been streamlined to create a flexible approach to both theory and modeling. The program includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics; emphasizing the connection between calculus and other fields.
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