Solutions for Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version
Problem 2CCE:
What is the difference between having a relative maximum at x=2 and having an absolute maximum at...Problem 3CCE:
Give three characterizations of what it means for the graph of f(x) to be concave up at x=2. Concave...Problem 15CCE:
Outline the procedure for solving an optimization problem.Problem 1RE:
Figure (1) contains the graph of f(x), the derivative of f(x). Use the graph to answer the following...Problem 2RE:
Figure (2) shows the graph of function f(x) and its tangent line at x=3. Find f(3),f(3), and f(3).Problem 3RE:
In Exercise 36, draw the graph of a function f(x) for which the function and its first derivative...Problem 4RE:
In Exercise 36, draw the graph of a function f(x) for which the function and its first derivative...Problem 5RE:
In Exercise 36, draw the graph of a function f(x) for which the function and its first derivative...Problem 6RE:
In Exercise 36, draw the graph of a function f(x) for which the function and its first derivative...Problem 7RE:
Exercise 712, refer to the graph in Fig. 3. List the labelled values of x at which the derivative...Problem 8RE:
Exercise 712, refer to the graph in Fig. 3. List the labelled values of x at which the derivative...Problem 9RE:
Exercise 712, refer to the graph in Fig. 3. List the labelled values of x at which the derivative...Problem 10RE:
Exercise 712, refer to the graph in Fig. 3. List the labelled values of x at which the derivative...Problem 11RE:
Exercise 712, refer to the graph in Fig. 3. List the labelled values of x at which the derivative...Problem 12RE:
Exercise 712, refer to the graph in Fig. 3. List the labelled values of x at which the derivative...Problem 13RE:
Properties of various functions are described next. In each case, draw some conclusion about the...Problem 14RE:
Properties of various functions are described next. In each case, draw some conclusion about the...Problem 15RE:
Properties of various functions are described next. In each case, draw some conclusion about the...Problem 16RE:
Properties of various functions are described next. In each case, draw some conclusion about the...Problem 17RE:
Properties of various functions are described next. In each case, draw some conclusion about the...Problem 18RE:
Properties of various functions are described next. In each case, draw some conclusion about the...Problem 19RE:
Properties of various functions are described next. In each case, draw some conclusion about the...Problem 21RE:
In Fig. 4 (a) and 4 (b), the t axis represents time in hours. a) When is f(t)=1? b) Find f(5). c)...Problem 22RE:
U.S. Electric Energy United States electrical energy production (in trillions of kilowatt-hours) in...Problem 33RE:
Sketch the following curves. y=2x3+3x2+1Problem 34RE:
Sketch the following curves. y=x332x26xProblem 35RE:
Sketch the following curves. y=x33x2+3x2Problem 36RE:
Sketch the following curves. y=100+36x6x2x3Problem 37RE:
Sketch the following curves. y=113+3xx213x3Problem 38RE:
Sketch the following curves. y=x33x29x+7Problem 39RE:
Sketch the following curves. y=13x32x25xProblem 40RE:
Sketch the following curves. y=x36x215x+50Problem 41RE:
Sketch the following curves. y=x42x2Problem 42RE:
Sketch the following curves. y=x44x3Problem 43RE:
Sketch the following curves. y=x5+20x+3(x0)Problem 44RE:
Sketch the following curves. y=12x+2x+1(x0)Problem 45RE:
Let f(x)=(x2+2)3/2. Show that the graph of f(x) has a possible relative extreme point at x=0.Problem 47RE:
Let f(x) be a function whose derivative is f(x)=11+x2 Note that f(x) is always positive. Show that...Problem 48RE:
Let f(x) be a function whose derivative is f(x)=5x2+1 Show that the graph of f(x) has an inflection...Problem 49RE:
Position Velocity and Acceleration A car traveling on a straight road and s(t) is the distance...Problem 50RE:
The water level in a reservoir varies during the year. Let h(t) be the depth (in feet) of water at...Problem 51RE:
Population near New York City Let f(x) be the number of people living within x miles of the center...Problem 53RE:
Find the maximum value of the function f(x)=26xx2,0x5, and give the value of x where this maximum...Problem 54RE:
Find the minimum value of the function g(t)=t26t+9,1t6.Problem 55RE:
Surface Area An open rectangular box is to be 4 feet long and have a volume of 200 cubic feet. Find...Problem 56RE:
Volume A closed rectangular box with a square base is to be constructed using two different types of...Problem 57RE:
Volume A long rectangular sheet of metal 30 inches wide is to be made into a gutter by turning up...Problem 58RE:
Maximizing the Total Yield A small orchard yields 25 bushels of fruit per tree when planted with 40...Problem 59RE:
Inventory Control A publishing company sells 400,000 copies of a certain book each year. Ordering...Problem 60RE:
Profit if the demand equation for a monopolist is p=150.02x and the cost function is C(x)=10x+300,...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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