Solutions for Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version
Problem 1E:
Exercises 1-4 refer to graphs (a)-(f) in Fig.19 Which functions are increasing for all x?Problem 2E:
Exercises 1-4 refer to graphs (a)-(f) in Fig.19 Which functions are decreasing for all x?Problem 3E:
Exercises 1-4 refer to graphs (a)-(f) in Fig.19 Which functions have the property that the slope...Problem 4E:
Exercises 1-4 refer to graphs (a)-(f) in Fig.19 Which functions have the property that the slope...Problem 5E:
Describe each of the following graphs. Your description should include each of the six categories...Problem 6E:
Describe each of the following graphs. Your description should include each of the six categories...Problem 7E:
Describe each of the following graphs. Your description should include each of the six categories...Problem 8E:
Describe each of the following graphs. Your description should include each of the six categories...Problem 9E:
Describe each of the following graphs. Your description should include each of the six categories...Problem 11E:
Describe each of the following graphs. Your description should include each of the six categories...Problem 13E:
Describe the way the slope changes as you move along the graph (from left to right) in Exercise 5.Problem 17E:
Exercise 17 and 18 refer to the graph in Fig 20. a. At which labelled points is the function...Problem 18E:
Exercise 17 and 18 refer to the graph in Fig 20. a. At which labelled points is the function...Problem 20E:
In Exercises 19-22, draw the graph of a function y=f(x) with the stated properties. The function...Problem 21E:
In Exercises 19-22, draw the graph of a function y=f(x) with the stated properties. The function...Problem 23E:
Annual World Consumption of Oil The annual world consumption of oil rises each year. Furthermore,...Problem 25E:
A Patients Temperature At noon, a childs temperature is 101F and is rising at an increasing rate. At...Problem 27E:
Blood Flow through the Brain One method of determining the level of blood flow through the brain...Problem 28E:
Pollution Suppose that some organic waste products are dumped into a lake at time t=0 and that the...Problem 32E:
Let P(t) be the population of a bacteria culture after t days and suppose that P(t) has the line...Problem 33E:
In Exercises 3336, sketch the graph of a function having the given properties. Defined for 0x10;...Problem 34E:
In Exercises 3336, sketch the graph of a function having the given properties. Relative maximum...Problem 35E:
In Exercises 3336, sketch the graph of a function having the given properties. Defined and...Problem 36E:
In Exercises 3336, sketch the graph of a function having the given properties. Defined for x0;...Problem 37E:
Consider a smooth curve with no undefined points. If it has two relative maximum points, must it...Problem 38E:
If the function f(x) has a relative minimum at x=a and a relative maximum at x=b, must f(a) be less...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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