Solutions for Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version
Problem 2CYU:
Find the slopes of the following lines. The line going through the points (2,5)and(2,8).Problem 27E:
In Exercises 2730, we specify a line by giving the slope and one point on the line. Start at the...Problem 29E:
In Exercises 2730, we specify a line by giving the slope and one point on the line. Start at the...Problem 33E:
In Exercises 3336, refer to a line of slope m. If you begin at a point on the line and move h units...Problem 34E:
In Exercises 3336, refer to a line of slope m. If you begin at a point on the line and move h units...Problem 35E:
In Exercises 3336, refer to a line of slope m. If you begin at a point on the line and move h units...Problem 37E:
In Exercises 37and38, we specify a line by giving the slope and one point on the line. We give the...Problem 38E:
In Exercises 37and38, we specify a line by giving the slope and one point on the line. We give the...Problem 39E:
In Exercises 37and38, we specify a line by giving the slope and one point on the line. We give the...Problem 43E:
Find the equation and sketch the graph of the following lines With slope 2 and y -intercept (0,1)Problem 47E:
Marginal Cost Let C(x)=12x+1100 denote the total cost (in dollars) of manufacturing x units of a...Problem 48E:
Refer to Exercise 47. Use the formula for C(x) to show directly that C(x+1)C(x)=12. Interpret your...Problem 49E:
Price of Gasoline The price of 1 gallon of unleaded gasoline at the pump dropped to 2.19 on January...Problem 50E:
Impact of Mad Cow Disease on Canadian Beef Exports The discovery of one case of bovine spongiform...Problem 51E:
Cost of Shipping and Handling An online bookstore charges 5 plus 3 of the purchase price of books...Problem 52E:
Quit Ratio In industry, the relationship between wages and the quit ratio of employees is defined to...Problem 53E:
Price Affects Sales When the owner of a gas station sets the price of 1 gallon of unleaded gasoline...Problem 56E:
Interpreting the Slope and y -Intercept A salesperson's weekly pay depends on the volume of sales....Problem 57E:
Interpreting the Slope and y -Intercept The demand equation for a manufacturer is y=.02x+7, where x...Problem 58E:
Converting Fahrenheit to Celsius Temperatures of 32 F and 212 F correspond to temperatures of 0 C...Problem 60E:
Refer to Exercise 59. If the patient's body eliminates the drug at the rate of 2 mL per hour, find...Problem 62E:
Diver's Ascent The diver in the previous exercise is supposed to stop for 5 minutes and decompress...Problem 64E:
Breakeven In order for a business to break even, revenue has to equal cost. Determine the minimum...Problem 65E:
If, for some constant m, f(x2)f(x1)x2x1=m for all x1x2, show that f(x)=mx+b, where b is some...Problem 66E:
a. Draw the graph of any function f(x) that passes through the point (3,2). b. Choose a point to 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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