Calculus Volume 117th EditionStrang, Gilbert Publisher: OpenStax CollegeISBN: 9781938168024
Calculus Volume 1
Solutions for Calculus Volume 1
Problem 54E:
For the following exercises, use the definition of a 65. Derivative to find f(x) . 54. f(x)=6Problem 55E:
For the following exercises, use the definition of a derivative to find f(x) . 55. f(x)=23xProblem 56E:
For the following exercises, use the definition of a derivative to find f(x) . 56. f(x)=2x7+1Problem 57E:
For the following exercises, use the definition of a derivative to find f(x) . 57. f(x)=4x2Problem 58E:
For the following exercises, use the definition of a derivative to find f(x) . 58. f(x)=5xx2Problem 59E:
For the following exercises, use the definition of a derivative to find f(x) . 59. f(x)=2xProblem 60E:
For the following exercises, use the definition of a derivative to find f(x) . 60. f(x)=x6Problem 61E:
For the following exercises, use the definition of a derivative to find f(x) 61. f(x)=9xProblem 62E:
For the following exercises, use the definition of a derivative to find f(x) 62. f(x)=x+1xProblem 63E:
For the following exercises, use the definition of a derivative to find f(x) 63. f(x)=1xProblem 64E:
For the following exercises, use the graph of y=f(x) to sketch the graph of its derivative f(x) 64.Problem 65E:
For the following exercises, use the graph of y=f(x) to sketch the graph of its derivative f(x) 65.Problem 66E:
For the following exercises, use the graph of y=f(x) to sketch the graph of its derivative f(x) 66.Problem 67E:
For the following exercises, use the graph of y=f(x) to sketch the graph of its derivative f(x) 67.Problem 68E:
For the following exercises, the given limit represents the derivative of a function y=f(x) at x =...Problem 69E:
For the following exercises, the given limit represents the derivative of a function y=f(x) at x =...Problem 70E:
For the following exercises, the given limit represents the derivative of a function y=f(x) at x =...Problem 71E:
For the following exercises, the given limit represents the derivative of a function y=f(x) at x =...Problem 72E:
For the following exercises, the given limit represents the derivative of a function y=f(x) at x =...Problem 73E:
For the following exercises, the given limit represents the derivative of a function y=f(x) at x =...Problem 74E:
For the following functions, sketch the graph and use the definition of a derivative to show that...Problem 75E:
For the following functions, sketch the graph and use the definition of a derivative to show that...Problem 76E:
For the following functions, sketch the graph and use the definition of a derivative to show that...Problem 77E:
For the following functions, sketch the graph and use the definition of a derivative to show that...Problem 78E:
For the following graphs, a. determine for which values of x=a the limxaf(x) exists but f is not...Problem 79E:
For the following graphs, a. determine for which values of x=a the limxaf(x) exists but f is not...Problem 80E:
Use the graph to evaluate a. f’(0.5), b. f’(0), c. f’(1), d. f’(2), and e. f’(3), if it exists.Problem 84E:
For the following exercises, use a calculator to graph f(x). Determine the function f(x) , then use...Problem 85E:
For the following exercises, use a calculator to graph f(x). Determine the function f(x) , then use...Problem 86E:
For the following exercises, use a calculator to graph f(x). Determine the function f(x) , then use...Problem 87E:
For the following exercises, use a calculator to graph f(x). Determine the function f(x) , then use...Problem 88E:
For the following exercises, use a calculator to graph f(x). Determine the function f(x) , then use...Problem 89E:
For the following exercises, use a calculator to graph f(x). Determine the function f(x) , then use...Problem 90E:
For the following exercises, describe what the two expressions represent in terms of each of the...Problem 91E:
For the following exercises, describe what the two expressions represent in terms of each of the...Problem 92E:
For the following exercises, describe what the two expressions represent in terms of each of the...Problem 93E:
For the following exercises, describe what the two expressions represent in terms of each of the...Problem 94E:
For the following exercises, describe what the two expressions represent in terms of each of the...Problem 95E:
For the following exercises, describe what the two expressions represent in terms of each of the...Problem 96E:
Sketch the graph of a function y=f(x) with all of the following properties: f(x)0 for 2x1 f(2)=0...Problem 97E:
Suppose temperature T in degrees Fahrenheit at a height x in feet above the ground is given by...Problem 98E:
Suppose the total profit of a company is y=P(x) thousand dollars when x units of an item are sold....Problem 99E:
The graph in the following figure models die number of people N(t) who have come down with the flu t...Problem 100E:
For the following exercises, use the following table, which show’s the height h of the Saturn V...Problem 101E:
[T] Construct a table of values for h' (t) and graph both h(t) and h’(t) on the same graph. (Hint:...Problem 102E:
[T] The best linear fit to the data is given by H(t)=7.229t4.905 , where H is the height of the...Problem 103E:
[T] The best quadratic fit to the data is given by G(t)=1.429t2+0.0857t0.1429 . where G is the...Browse All Chapters of This Textbook
Chapter 1 - Functions And GraphsChapter 1.1 - Review Of FunctionsChapter 1.2 - Basic Classes Of FunctionsChapter 1.3 - Trigonometric FunctionsChapter 1.4 - Inverse FunctionsChapter 1.5 - Exponential And Logarithmic FunctionsChapter 2 - LimitsChapter 2.1 - A Preview Of CalculusChapter 2.2 - The Limit Of A FunctionChapter 2.3 - The Limit Laws
Chapter 2.4 - ContinuityChapter 2.5 - The Precise Definition Of A LimitChapter 3 - DerivativesChapter 3.1 - Defining The DerivativeChapter 3.2 - The Derivative As A FunctionChapter 3.3 - Differentiation RulesChapter 3.4 - Derivatives As Rates Of ChangeChapter 3.5 - Derivatives Of Trigonometric FunctionsChapter 3.6 - The Chain RuleChapter 3.7 - Derivatives Of Inverse FunctionsChapter 3.8 - Implicit DifferentiationChapter 3.9 - Derivatives Of Exponential And Logarithmic FunctionsChapter 4 - Applications Of DerivativesChapter 4.1 - Related RatesChapter 4.2 - Linear Approximations And DifferentialsChapter 4.3 - Maxima And MinimaChapter 4.4 - The Mean Value TheoremChapter 4.5 - Derivatives And The Shape Of A GraphChapter 4.6 - Limits At Infinity And AsymptotesChapter 4.7 - Applied Optimization ProblemsChapter 4.8 - L'hopitars RuleChapter 4.9 - Newton's MethodChapter 4.10 - AntiderivativesChapter 5 - IntegrationChapter 5.1 - Approximating AreasChapter 5.2 - The Definite IntegralChapter 5.3 - The Fundamental Theorem Of CalculusChapter 5.4 - Integration Formulas And The Net Change TheoremChapter 5.5 - SubstitutionChapter 5.6 - Integrals Involving Exponential And Logarithmic FunctionsChapter 5.7 - Integrals Resulting In Inverse Trigonometric FunctionsChapter 6 - Applications Of IntegrationChapter 6.1 - Areas Between CurvesChapter 6.2 - Determining Volumes By SlicingChapter 6.3 - Volumes Of Revolution: Cylindrical ShellsChapter 6.4 - Arc Length Of A Curve And Surface AreaChapter 6.5 - Physical ApplicationsChapter 6.6 - Moments And Centers Of MassChapter 6.7 - Integrals, Exponential Functions, And LogarithmsChapter 6.8 - Exponential Growth And DecayChapter 6.9 - Calculus Of The Hyperbolic Functions
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