Solutions for Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version
Problem 1CYU:
Solution can be found following the section exercises. Suppose that x and y are related by the...Problem 2CYU:
Solution can be found following the section exercises. Suppose that x and y are related by the...Problem 1E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 2E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 3E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 4E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 5E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 6E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 7E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 8E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 9E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 10E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 11E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 12E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 13E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 14E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 15E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 16E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 17E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 18E:
In Exercise 1-18, suppose that x and y are related by the given equation and use implicit...Problem 19E:
Use implicit differentiation of the equation in Exercise 19 24 to determine the slope of the graph...Problem 20E:
Use implicit differentiation of the equation in Exercise 19 24 to determine the slope of the graph...Problem 21E:
Use implicit differentiation of the equation in Exercise 19 24 to determine the slope of the graph...Problem 22E:
Use implicit differentiation of the equation in Exercise 19 24 to determine the slope of the graph...Problem 23E:
Use implicit differentiation of the equation in Exercise 19 24 to determine the slope of the graph...Problem 24E:
Use implicit differentiation of the equation in Exercise 19 24 to determine the slope of the graph...Problem 25E:
Find the equation of the tangent line to the graph of x2y4=1 at the point (4,12) and at the point...Problem 26E:
Find the equation of the tangent line to the graph of x4y2=144 at the point (2,3) and at the point...Problem 27E:
Slope of the Lemniscate The graph of x4+2x2y2+y4=4x24y2 is the lemniscate in the figure. a. Find...Problem 28E:
The graph of x4+2x2y2+y4=9x29y2 is a lemniscate similar to that in figure 6. a. Find dydx by...Problem 29E:
Marginal Rate of Substitution Suppose that x and y represents the amounts of two basic inputs for a...Problem 30E:
Demand Equation Suppose that x and y represents the amounts of two basic inputs for a production...Problem 31E:
In Exercise 31 36, suppose that x and y are both differentiable functions of t and are related by...Problem 32E:
In Exercise 31 36, suppose that x and y are both differentiable functions of t and are related by...Problem 33E:
In Exercise 31 36, suppose that x and y are both differentiable functions of t and are related by...Problem 35E:
In Exercise 31 36, suppose that x and y are both differentiable functions of t and are related by...Problem 39E:
Demand Equation Suppose that the price p (in dollars) and the weekly sales x (in thousands of units)...Problem 40E:
Demand Equation Suppose that the price p (in dollars) and the weekly sales x (in thousands of units)...Problem 41E:
Advertising Affects Revenue The monthly advertising revenue A and the monthly circulation x of a...Problem 42E:
Rate of Change of Price Suppose that in Boston the wholesale price p of oranges (in dollars per...Problem 43E:
Related Rates Figure 7 shows a 10- foot ladder leaning against a wall. a. Use the Pythagorean...Problem 44E:
Related Rates An airplane flying 390 feet per second at an altitude of 5000 feet flew directly over...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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