Solutions for Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version
Problem 1CCE:
State the product rule and quotient rule.Problem 2RE:
Differentiate the following functions. y=2(5x)3(6x1)Problem 3RE:
Differentiate the following functions. y=x(x51)3Problem 5RE:
Differentiate the following functions. y=5(x1)4(x2)2Problem 6RE:
Differentiate the following functions. y=xx+4Problem 8RE:
Differentiate the following functions. y=1(x2+5x+1)6Problem 9RE:
Differentiate the following functions. y=x26xx2Problem 10RE:
Differentiate the following functions. y=2x23xProblem 11RE:
Differentiate the following functions. y=(3x2x3)2Problem 12RE:
Differentiate the following functions. y=x3+xx2xProblem 13RE:
Let f(x)=(3x+1)4(3x)5. Find all x such that f(x)=0.Problem 14RE:
Let f(x)=x2+1x2+5. Find all x such that f(x)=0.Problem 15RE:
Find the equation of the line tangent to the graph of y=(x31)(x2+1)4 at the point where x=1.Problem 16RE:
Find the equation of the line tangent to the graph of y=x34+x2 at the point where x=0.Problem 17RE:
Minimizing Area A botanical display is to be constructed as a rectangular region with a river as one...Problem 18RE:
Repeat Exercise 17, with the sidewalk on the inside of all four sides. In this case, the 800-square-...Problem 19RE:
Cost function A store estimates that its cost when selling x lamps per day is C dollars, where...Problem 20RE:
Rate of Change of Taxes A company pays y dollars in taxes when its annual profit is P dollars. If y...Problem 21RE:
In Exercise 21-23, find a formula for ddxf(g(x)), where f(x) is a function such that f(x)=1/(x2+1)...Problem 22RE:
In Exercise 21-23, find a formula for ddxf(g(x)), where f(x) is a function such that f(x)=1/(x2+1)...Problem 23RE:
In Exercise 21-23, find a formula for ddxf(g(x)), where f(x) is a function such that f(x)=1/(x2+1)...Problem 24RE:
In Exercise 24-26, find a formula for ddxf(g(x)), where f(x) is a function such that f(x)=x1x2...Problem 25RE:
In Exercise 24-26, find a formula for ddxf(g(x)), where f(x) is a function such that f(x)=x1x2...Problem 26RE:
In Exercise 24-26, find a formula for ddxf(g(x)), where f(x) is a function such that f(x)=x1x2...Problem 27RE:
In Exercise 27-29, find dydx, where y is a function of u such that dydu=uu2+1. State the answer in...Problem 28RE:
In Exercise 27-29, find dydx, where y is a function of u such that dydu=uu2+1. State the answer in...Problem 29RE:
In Exercise 27-29, find dydx, where y is a function of u such that dydu=uu2+1. State the answer in...Problem 33RE:
Exercises 33 38 refer to the graphs of the functions f(x) and g(x) in Fig. 2. Determine h(1) and...Problem 34RE:
Exercises 33 38 refer to the graphs of the functions f(x) and g(x) in Fig. 2. Determine h(1) and...Problem 35RE:
Exercises 33 38 refer to the graphs of the functions f(x) and g(x) in Fig. 2. Determine h(1) and...Problem 36RE:
Exercises 33 38 refer to the graphs of the functions f(x) and g(x) in Fig. 2. Determine h(1) and...Problem 37RE:
Exercises 33 38 refer to the graphs of the functions f(x) and g(x) in Fig. 2. Determine h(1) and...Problem 38RE:
Exercises 33 38 refer to the graphs of the functions f(x) and g(x) in Fig. 2. Determine h(1) and...Problem 39RE:
Revenue Function The revenue, R, that a company receives is a function of the weekly sales, x. Also,...Problem 40RE:
Amount of Drug Usage The amount, A, of anesthetics that a certain hospital uses each week is a...Problem 41RE:
The graph of x2/3+y2/3=8 is the astroid in Fig. 3 Find dydx by implicit differentiation. Find the...Problem 42RE:
Slope of the Folium of Descartes The graph of x3+y3=9xy is is folium of Descartes shown in Fig. 4...Problem 43RE:
Slope of the Folium of Descartes The graph of x3+y3=9xy is is folium of Descartes shown in Fig. 4...Problem 44RE:
In Exercises 43-46, x and y are related by the given equation. Use implicit differentiation to...Problem 45RE:
In Exercises 43-46, x and y are related by the given equation. Use implicit differentiation to...Problem 46RE:
In Exercises 43-46, x and y are related by the given equation. Use implicit differentiation to...Problem 47RE:
Cost Analysis and Production A factorys weekly production costs y and its weekly production quantity...Problem 48RE:
Use of Books at a Library A town library estimates that, when the population is x thousand persons,...Problem 49RE:
Demand equation Suppose that the price p and quantity x of a certain commodity satisfy the demand...Problem 50RE:
Volume of an Oil Spill An offshore oil well is leaking oil onto the ocean surface, forming a...Browse All Chapters of This Textbook
Chapter 0 - FunctionsChapter 0.1 - Functions And Their GraphsChapter 0.2 - Some Important FunctionsChapter 0.3 - The Algebra Of FunctionsChapter 0.4 - Zeros Of Functions—the Quadratic Formula And FactoringChapter 0.5 - Exponents And Power FunctionsChapter 0.6 - Functions And Graphs In ApplicationsChapter 1 - The DerivativeChapter 1.1 - The Slope Of A Straight LineChapter 1.2 - The Slope Of A Curve At A Point
Chapter 1.3 - The Derivative And LimitsChapter 1.4 - Limits And The DerivativeChapter 1.5 - Differentiability And ContinuityChapter 1.6 - Some Rules For DifferentiationChapter 1.7 - More About DerivativesChapter 1.8 - The Derivative As A Rate Of ChangeChapter 2 - Applications Of The DerivativeChapter 2.1 - Describing Graphs Of FunctionsChapter 2.2 - The First- And Second-derivative RulesChapter 2.3 - The First- And Second-derivative Tests And Curve SketchingChapter 2.4 - Curve Sketching (conclusion)Chapter 2.5 - Optimization ProblemsChapter 2.6 - Further Optimization ProblemsChapter 2.7 - Applications Of Derivatives To Business And EconomicsChapter 3 - Techniques Of DifferentiationChapter 3.1 - The Product And Quotient RulesChapter 3.2 - The Chain RuleChapter 3.3 - Implicit Differentiation And Related RatesChapter 4 - The Exponential And Natural Logarithm FunctionsChapter 4.1 - Exponential FunctionsChapter 4.2 - The Exponential Function ExChapter 4.3 - Differentiation Of Exponential FunctionsChapter 4.4 - The Natural Logarithm FunctionChapter 4.5 - The Derivative Of Ln XChapter 4.6 - Properties Of The Natural Logarithm FunctionChapter 5 - Applications Of The Exponential And Natural Logarithm FunctionsChapter 5.1 - Exponential Growth And DecayChapter 5.2 - Compound InterestChapter 5.3 - Applications Of The Natural Logarithm Function To EconomicsChapter 5.4 - Further Exponential ModelsChapter 6 - The Definite IntegralChapter 6.1 - AntidifferentiationChapter 6.2 - The Definite Integral And Net Change Of A FunctionChapter 6.3 - The Definite Integral And Area Under A GraphChapter 6.4 - Areas In The Xy-planeChapter 6.5 - Applications Of The Definite IntegralChapter 7 - Functions Of Several VariablesChapter 7.1 - Examples Of Functions Of Several VariablesChapter 7.2 - Partial DerivativesChapter 7.3 - Maxima And Minima Of Functions Of Several VariablesChapter 7.4 - Lagrange Multipliers And Constrained OptimizationChapter 7.5 - The Method Of Least SquaresChapter 7.6 - Double IntegralsChapter 8 - The Trigonometric FunctionsChapter 8.1 - Radian Measure Of AnglesChapter 8.2 - The Sine And The CosineChapter 8.3 - Differentiation And Integration Of Sin T And Cos TChapter 8.4 - The Tangent And Other Trigonometric FunctionsChapter 9 - Techniques Of IntegrationChapter 9.1 - Integration By SubstitutionChapter 9.2 - Integration By PartsChapter 9.3 - Evaluation Of Definite IntegralsChapter 9.4 - Approximation Of Definite IntegralsChapter 9.5 - Some Applications Of The IntegralChapter 9.6 - Improper IntegralsChapter 10 - Differential EquationsChapter 10.1 - Solutions Of Differential EquationsChapter 10.2 - Separation Of VariablesChapter 10.3 - First-order Linear Differential EquationsChapter 10.4 - Applications Of First-order Linear Differential EquationsChapter 10.5 - Graphing Solutions Of Differential EquationsChapter 10.6 - Applications Of Differential EquationsChapter 10.7 - Numerical Solution Of Differential EquationsChapter 11 - Taylor Polynomials And Infinite SeriesChapter 11.1 - Taylor PolynomialsChapter 11.2 - The Newton–raphson AlgorithmChapter 11.3 - Infinite SeriesChapter 11.4 - Series With Positive TermsChapter 11.5 - Taylor SeriesChapter 12 - Probability And CalculusChapter 12.1 - Discrete Random VariablesChapter 12.2 - Continuous Random VariablesChapter 12.3 - Expected Value And VarianceChapter 12.4 - Exponential And Normal Random VariablesChapter 12.5 - Poisson And Geometric Random Variables
Book Details
Calculus & Its Applications builds intuition with key concepts of calculus before the analytical material. For example, the authors explain the derivative geometrically before they present limits, and they introduce the definite integral intuitively via the notion of net change before they discuss Riemann sums. The strategic organization of topics makes it easy to adjust the level of theoretical material covered. The significant applications introduced early in the course serve to motivate students and make the mathematics more accessible. Another unique aspect of the text is its intuitive use of differential equations to model a variety of phenomena in Chapter 5, which addresses applications of exponential and logarithmic functions.
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