Solutions for Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version
Problem 1CYU:
Differentiate f(x)=1ln(x4+5).Problem 2CYU:
Differentiate f(x)=ln(lnx).Problem 2E:
Differentiate the following functions. y=lnxln3Problem 3E:
Differentiate the following functions. y=x2lnx2Problem 4E:
Differentiate the following functions. y=3lnxxProblem 5E:
Differentiate the following functions. y=exlnxProblem 6E:
Differentiate the following functions. y=e1+lnxProblem 7E:
Differentiate the following functions. y=lnxxProblem 9E:
Differentiate the following functions. y=lnx2Problem 11E:
Differentiate the following functions. y=ln(1x)Problem 13E:
Differentiate the following functions. y=ln(3x4x2)Problem 15E:
Differentiate the following functions. y=1lnxProblem 16E:
Differentiate the following functions. y=lnxln2xProblem 17E:
Differentiate the following functions. y=lnxln2xProblem 18E:
Differentiate the following functions. y=(lnx)2Problem 21E:
Find the second derivatives. d2dt2(t2lnt)Problem 22E:
Find the second derivatives. d2dt2ln(lnt)Problem 23E:
The graph of f(x)=(lnx)/x is shown in Fig.4. Find the coordinates of the maximum point.Problem 24E:
The graph of f(x)=x/(lnx+x) is shown in Fig.5. Find the coordinates of the minimum point.Problem 26E:
The function f(x)=(lnx+1)/x has a relative extreme point for x0. Find the coordinates of the point....Problem 27E:
Determine the domain of definition of the given function. a. f(t)=ln(lnt) b. f(t)=ln(ln(lnt))Problem 29E:
Find the coordinates of the relative extreme point of y=x2lnx, x0. Then, use the second derivative...Problem 30E:
Repeat the previous exercise with y=xlnx.Problem 31E:
The graphs of y=x+lnx and y=ln2x are shown in Fig.6. a. Show that both functions are increasing for...Problem 35E:
A Demand Equation If the demand equation for a certain commodity is p=45/(lnx), determine the...Problem 36E:
Total Revenue Suppose that the total revenue function for a manufacturer is R(x)=300ln(x+1), so the...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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