Solutions for Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version
Problem 1CYU:
Differentiate tet2Problem 2CYU:
Differentiate [ e3x(1+e6x) ]12.Problem 2E:
Differentiate the following functions. f(x)=e3x2Problem 5E:
Differentiate the following functions. f(x)=eexProblem 6E:
Differentiate the following functions. f(x)=e1xProblem 7E:
Differentiate the following functions. f(x)=exProblem 9E:
Differentiate the following functions. f(x)=7ex7Problem 10E:
Differentiate the following functions. f(x)=10ex25Problem 16E:
Differentiate the following functions. f(x)=eeexProblem 19E:
Differentiate the following functions. f(x)=ex+1Problem 20E:
Differentiate the following functions. f(x)=eexProblem 27E:
In Exercises 27-32, find the values of x at which the function has a possible relative maximum or...Problem 28E:
In Exercises 27-32, find the values of x at which the function has a possible relative maximum or...Problem 29E:
In Exercises 27-32, find the values of x at which the function has a possible relative maximum or...Problem 30E:
In Exercises 27-32, find the values of x at which the function has a possible relative maximum or...Problem 31E:
In Exercises 27-32, find the values of x at which the function has a possible relative maximum or...Problem 32E:
In Exercises 27-32, find the values of x at which the function has a possible relative maximum or...Problem 33E:
An Investment Portfolio The value of an investment portfolio consisting of two stocks is given by...Problem 34E:
Depreciation of Assets The value of the computer t years after purchase is v(t)=2000e0.35t dollars....Problem 35E:
The Most Expensive Artwork to Date The highest price ever paid for an artwork at auction was for...Problem 36E:
Appreciation of Assets A painting purchased in 2015 for 100,000 is estimated to be worth...Problem 37E:
Velocity and Acceleration The velocity of the parachutist during free fall is f(t)=60(1e0.17t)...Problem 38E:
Velocity and Acceleration Suppose the velocity of the parachutist is v(t)=65(1e0.16t) meters per...Problem 39E:
Heights of a Plant The height of a certain plant, in inches, after t weeks is f(t)=1.05+e0.4t. The...Problem 40E:
Heights of a Plant The length of a certain weed, in centimeters, after t weeks is f(x)=6.2+5e0.5t....Problem 41E:
Gompertz Growth Curve Let aandb be positive numbers. A curve whose equation is y=eaebx. is called a...Problem 42E:
Find dydx if y=e(110)ex2.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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