Calculus: Single And Multivariable, 7e ...7th EditionDeborah Hughes-Hallett Publisher: Wiley (wileyplus Products) (edition 7)ISBN: 9781119343998
Calculus: Single And Multivariable, 7e ...
Solutions for Calculus: Single And Multivariable, 7e Wileyplus Registration Card + Loose-leaf Print Companion
Problem 1E:
Let f(x) = 7. Using the denition of the derivative, show that f(x) = 0 for all values of x.Problem 3E:
For Exercises 35, determine if the derivative rules from this section apply. If they do, find the...Problem 4E:
For Exercises 35, determine if the derivative rules from this section apply. If they do, find the...Problem 5E:
For Exercises 35, determine if the derivative rules from this section apply. If they do, find the...Problem 6E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 7E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 8E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 9E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 10E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 11E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 12E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 13E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 14E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 15E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 16E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 17E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 18E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 19E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 20E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 21E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 22E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 23E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 24E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 25E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 26E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 27E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 28E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 29E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 30E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 31E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 32E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 33E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 34E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 35E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 36E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 37E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 38E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 39E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 40E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 41E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 42E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 43E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 44E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 45E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 46E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 47E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 48E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 49E:
For Exercises 649, find the derivatives of the given functions. Assume that a, b, c, and k are...Problem 50E:
In Exercises 5057, use the tangent line approximation. Given f(4) = 5, f(4) = 7, approximate...Problem 51E:
In Exercises 5057, use the tangent line approximation. Given f(4) = 5, f(4) = 7, approximate...Problem 52E:
In Exercises 5057, use the tangent line approximation. Given f(5) = 3, f(5) = 2, approximate...Problem 53E:
In Exercises 5057, use the tangent line approximation. Given f(2) = 4, f(2) = 3, approximate...Problem 54E:
In Exercises 5057, use the tangent line approximation. Given f(3) = 4, f(3) = 2, approximate...Problem 55E:
In Exercises 5057, use the tangent line approximation. Given f(3) = 4, f(3) = 2, approximate...Problem 56E:
In Exercises 5057, use the tangent line approximation. Given f(x)=x4x2+3, approximate f(1.04).Problem 57E:
In Exercises 5057, use the tangent line approximation. Given f(x)=x3+x26, approximate f(0.97).Problem 58E:
If f(x)=6x42x+7, find f(x), f(x), and f(x).Problem 59E:
(a) Let f(x) = x7. Find f(x), f(x), and f(x). (b) Find the smallest n such that f (n)(x) = 0.Problem 60E:
If p(t)=t3+2t2t+4, find d2p/dt2 and d3p/dt3.Problem 61E:
If w(x)=x+(1/x), find d2w/dx2 and d3w/dx3.Problem 62E:
For Problems 6267, determine if the derivative rules from this section apply. If they do, find the...Problem 63E:
For Problems 6267, determine if the derivative rules from this section apply. If they do, find the...Problem 64E:
For Problems 6267, determine if the derivative rules from this section apply. If they do, find the...Problem 65E:
For Problems 6267, determine if the derivative rules from this section apply. If they do, find the...Problem 66E:
For Problems 6267, determine if the derivative rules from this section apply. If they do, find the...Problem 67E:
For Problems 6267, determine if the derivative rules from this section apply. If they do, find the...Problem 68E:
If f(x)=(3x+8)(2x5), find f(x) and f(x).Problem 69E:
Find the equation of the line tangent to the graph of f at (1, 1), where f is given by...Problem 72E:
(a) Find the equation of the tangent line to f(x) = x3 at the point where x = 2. (b) Graph the...Problem 73E:
(a) Use Figure 3.8 to rank the quantities f (1), f (0), f (1), f (4) from smallest to largest. (b)...Problem 74E:
The graph of y=x39x216x+1 has a slope of 5 at two points. Find the coordinates of the points.Problem 77E:
(a) Find the eighth derivative of f(x)=x7+5x54x3+6x7. Think ahead! (The nth derivative, f(n)(x), is...Problem 78E:
For the functions in Problems 7881: (a) Find the derivative at x = 1. (b) Find the second derivative...Problem 79E:
For the functions in Problems 7881: (a) Find the derivative at x = 1. (b) Find the second derivative...Problem 80E:
For the functions in Problems 7881: (a) Find the derivative at x = 1. (b) Find the second derivative...Problem 81E:
For the functions in Problems 7881: (a) Find the derivative at x = 1. (b) Find the second derivative...Problem 82E:
With t in years since 2016, the height of a sand dune (in centimeters) is f(t) = 700 3t 2. Find...Problem 83E:
A rubber balloon contains neon. As the air pressure, P (in atmospheres), outside the balloon...Problem 84E:
A ball is dropped from the top of the Empire State building to the ground below. The height, y, of...Problem 85E:
At a time t seconds after it is thrown up in the air, a tomato is at a height of f(t)=4.9t2+25t+3...Problem 86E:
Let f(t) and g(t) give, respectively, the amount of water (in acre-feet) in two different reservoirs...Problem 87E:
A jkulhlaup is the rapid draining of a glacial lake when an ice dam bursts. The maximum outflow...Problem 88E:
(a) For y = kxn, show that near any point x = a, we have y/ynx/a. (b) Interpret this relationship in...Problem 89E:
In Problems 8992, use the fact that for a power function y = kxn, for small changes, the percent...Problem 90E:
In Problems 8992, use the fact that for a power function y = kxn, for small changes, the percent...Problem 91E:
In Problems 8992, use the fact that for a power function y = kxn, for small changes, the percent...Problem 92E:
In Problems 8992, use the fact that for a power function y = kxn, for small changes, the percent...Problem 93E:
The depth, h (in mm), of the water runoff down a slope during steady rain3 is a function of the...Problem 94E:
If M is the mass of the earth and G is a constant, the acceleration due to gravity, g, at a distance...Problem 95E:
The period, T, of a pendulum is given in terms of its length, l, by T=2lg, where g is the...Problem 96E:
(a) Use the formula for the area of a circle of radius r, A = r2, to find dAdr. (b) The result from...Problem 98E:
Suppose W is proportional to r3. The derivative dWdr is proportional to what power of r?Problem 99E:
Given a power function of the form f(x) = axn, with f(2) = 3 and f(4) = 24, find n and a.Problem 100E:
(a) Find the value of a making f(x) continuous at x = 1: f(x)={ax0x1x2+31x2. (b) With the value of a...Problem 101E:
Let f(x)=x3+3x22x+1 and g(x)=x3+3x22x4. (a) Show that the derivatives of f(x) and g(x) are the same....Problem 102E:
Let f(x)=x43x2+1. (a) Show that f(x) is an even function. (b) Show that f (x) is an odd function....Problem 103E:
In Problems 103104, explain what is wrong with the statement. The only function that has derivative...Problem 104E:
In Problems 103104, explain what is wrong with the statement. The derivative of f(x) = 1/x2 is f(x)...Problem 105E:
In Problems 105107, give an example of: Two functions f(x) and g(x) such that ddx(f(x)+g(x))=2x+3.Problem 106E:
In Problems 105107, give an example of: A function whose derivative is g(x) = 2 and whose graph has...Problem 107E:
In Problems 105107, give an example of: A function which has second derivative equal to 6...Problem 108E:
In Problems 108110, is the statement true or false? Give an explanation for your answer. The...Problem 109E:
In Problems 108110, is the statement true or false? Give an explanation for your answer. The...Problem 110E:
In Problems 108110, is the statement true or false? Give an explanation for your answer. If f(2) =...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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