Solutions for Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version
Problem 1CYU:
Let f(t) be the temperature (In degrees Celsius) of a liquid at time t (In hours). The rate of...Problem 2CYU:
Let f(t) be the temperature (in degrees Celsius) of a liquid at time t (In hours). The rate of...Problem 3CYU:
Let f(t) be the temperature (in degrees Celsius) of a liquid at time t (In hours). The rate of...Problem 1E:
If f(x)=x2+3x, calculate the average rate of change of f(x) over the following intervals 1x2, 1x1.5,...Problem 2E:
If f(x)=3x2+2, calculate the average rate of change of f(x) over the following intervals 0x.5, 0x.1,...Problem 3E:
Average and Instantaneous Rates of Change Suppose that f(x)=4x2 What is the average rate of change...Problem 4E:
Average and Instantaneous Rates of Change Suppose that f(x)=6/x What is the average rate of change...Problem 5E:
Average and Instantaneous Rates of Change Suppose that f(t)=t2+3t7 What is the average rate of...Problem 6E:
Average and Instantaneous Rates of Change Suppose that f(t)=3t+212t What is the average rate of...Problem 7E:
Motion of an Object An object moving in a straight line travels s(t) kilometres in t hours, where...Problem 8E:
Effect of Advertising on Sales After an advertising campaign, the sales of a product often increase...Problem 9E:
Average Daily Output An analysis of the daily output of a factory assembly line shows that about...Problem 11E:
Maximum Height A toy rocket is fired straight up in the air. Let s(t)=6t2+72t denote its position in...Problem 12E:
Analysis of a Moving Particle Refer to Fig.6, where s(t) represents the position of a car moving in...Problem 13E:
Position of Toy Rocket A toy rocket fired straight up into the air has height s(t)=160t16t2 feet...Problem 14E:
Height of a Helicopter A helicopter is rising straight up in the air. Its distance from the ground t...Problem 15E:
Height of a Ball Let s(t) be the height (in feet) after t seconds of a ball thrown straight up in...Problem 16E:
Average Speed Table 2 gives a cars trip odometer reading (in miles) at 1 hour into a trip and at...Problem 17E:
Velocity and Position A particle is moving in a straight line in such a way that its position at...Problem 18E:
Interpreting Rates of Change on a Graph A car is traveling from New York to Boston and is partway...Problem 19E:
Estimating the Values of a function If f(100)=5000 and f(100)=10, estimate each of the following. a....Problem 20E:
Estimating the Values of a function If f(25)=10 and f(25)=2, estimate each of the following. a....Problem 21E:
Temperature of a Cup of Coffee Let f(t) be the temperature of a cup of coffee t minutes after it has...Problem 22E:
Rate of Elimination of a Drug Suppose that 5 mg of a drug is injected into the bloodstream. Let f(t)...Problem 23E:
Price Affects Sales Let f(p) be the number of cars sold when the price is p dollars per car....Problem 24E:
Advertising Affects Salesdollars are spent on advertising. Interpret t Let f(x) be the number of...Problem 25E:
Rate of Sales Let f(x) be the number (in thousands) of computers sold when the price is x hundred...Problem 26E:
Marginal Cost Let C(x) be the cost (in dollars) of manufacturing x items. Interpret the statements...Problem 28E:
Price of a Companys Stock Let f(x) be the value in dollars of one share of a company x days since...Problem 29E:
Marginal Cost Analysis Consider the cost function C(x)=6x2+14x+18 (thousand dollars). What is the...Problem 31E:
Health Expenditures National health expenditures (in billions of dollars) from 1980 to 1998 are...Problem 32E:
Velocity and Acceleration In an 8-second test run, a vehicle accelerates for several seconds and...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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