CALCULUS, VOLUME 1 (OER)17th EditionOpenStax Publisher: XANEDU CISBN: 2810022307715
CALCULUS, VOLUME 1 (OER)
Solutions for CALCULUS,VOLUME 1 (OER)
Problem 1E:
For the following exercises, find the quantities for the given equation. 1. Find dydt at x=1 and...Problem 2E:
For the following exercises, find the quantities for the given equation. 2. Find dxdt at x=2 and...Problem 3E:
For the following exercises, find the quantities for the given equation. Find dzdt at (x, y) = (1,...Problem 4E:
For the following exercises, sketch the situation if necessary and used related rates to solve for...Problem 5E:
For the following exercises, sketch the situation if necessary and used related rates to solve for...Problem 6E:
A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1...Problem 7E:
Two airplanes are flying in the air at the same height: airplane A is flying east at 250 mi/h and...Problem 8E:
You and a friend are riding your bikes to a restaurant that you think is east; your friend thinks...Problem 9E:
Two buses are driving along parallel freeways that are 5 mi apart, one heading east and the other...Problem 10E:
A 6-ft-tall person walks away from a 10-ft lamppost at a constant rate of 3 ft/sec. What is the rate...Problem 11E:
Using the previous problem, what is the rate at which the tip of the shadow moves away from the...Problem 12E:
A 5-ft-tall person walks toward a wall at a rate of 2 ft/ sec. A spotlight is located on the ground...Problem 13E:
Using the previous problem, what is the rate at which the shadow changes when the person is 10 ft...Problem 14E:
A helicopter starting on the ground is rising directly into the air at a rate of 25 ft/sec. You are...Problem 15E:
Using the previous problem, what is the rate at which the distance between you and the helicopter is...Problem 16E:
For the following exercises, draw and label diagrams to help solve the related-rates problems. 16....Problem 17E:
For the following exercises, draw and label diagrams to help solve the related-rates problems. 17....Problem 18E:
For the following exercises, draw and label diagrams to help solve the related-rates problems. 18....Problem 19E:
For the following exercises, draw and label diagrams to help solve the related-rates problems. 19....Problem 20E:
For the following exercises, draw and label diagrams to help solve the related-rates problems. 20....Problem 21E:
For the following exercises, draw and label diagrams to help solve the related-rates problems. 21....Problem 22E:
For the following exercises, draw and label diagrams to help solve the related-rates problems. 22....Problem 23E:
For the following exercises, draw and label diagrams to help solve the related-rates problems. 23. A...Problem 24E:
For the following exercises, draw and label diagrams to help solve the related-rates problems. 24. A...Problem 25E:
For the following exercises, consider a tight cone that is leaking water. The dimensions of die...Problem 26E:
For the following exercises, consider a right cone that is leaking water. The dimensions of the...Problem 27E:
For the following exercises, consider a right cone that is leaking water. The dimensions of the...Problem 28E:
For the following exercises, consider a tight cone that is leaking water. The dimensions of die...Problem 29E:
For the following exercises, consider a right cone that is leaking water. The dimensions of the...Problem 30E:
A trough has ends shaped like isosceles triangles, with width 3 m and height 4 m, and the trough is...Problem 31E:
A tank is shaped like an upside-down square pyramid, with base of 4 m by 4 m and a height of 12 m...Problem 32E:
For the following problems, consider a pool shaped like the bottom half of a sphere, that is being...Problem 33E:
For the following problems, consider a pool shaped like the bottom half of a sphere, that is being...Problem 34E:
For the following problems, consider a pool shaped like the bottom half of a sphere, that is being...Problem 35E:
For the following problems, consider a pool shaped like the bottom half of a sphere, that is being...Problem 36E:
For the following problems, consider a pool shaped like the bottom half of a sphere, that is being...Problem 37E:
For the following exercises, draw the situations and solve the related-rate problems. 37. You are...Problem 38E:
For the following exercises, draw the situations and solve the related-rate problems. 38. You stand...Problem 39E:
A lighthouse, L, is on an island 4 mi away from the closest point, P, on the beach (see the...Problem 40E:
Using the same setup as the previous problem, determine at what rate the beam of light moves across...Problem 41E:
You are walking to a bus stop at a right-angle corner. You move north at a rate of 2 m/sec and are...Problem 42E:
[T] A batter hits a ball toward third base at 75 ft/sec and runs toward first base at a rate of 24...Problem 43E:
[T] A batter hits a ball toward second base at 80 ft/sec and runs toward first base at a rate of 30...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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