Calculus, Early Transcendentals, Intern...8th EditionJames Stewart Publisher: Cengage LearningISBN: 9781305272378
Calculus, Early Transcendentals, Intern...
Solutions for Calculus, Early Transcendentals, International Metric Edition
Problem 1E:
Consider the following problem: Find two numbers whose sum is 23 and whose product is a maximum. (a)...Problem 4E:
The sum of two positive numbers is 16. What is the smallest possible value of the sum of their...Problem 5E:
What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for 1 x ...Problem 7E:
Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible.Problem 8E:
Find the dimensions of a rectangle with area 1000 m2 whose perimeter is as small as possible.Problem 9E:
A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the...Problem 10E:
The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is...Problem 11E:
Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area...Problem 12E:
Consider the following problem: A box with an open top is to be constructed from a square piece of...Problem 13E:
A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide...Problem 14E:
A box with a square base and open top must have a volume of 32,000 cm3. Find the dimensions of the...Problem 15E:
If 1200 cm2 of material is available to make a box with a square base and an open top, find the...Problem 16E:
A rectangular storage container with an open top is to have a volume of 10 m3. The length of its...Problem 17E:
Do Exercise 16 assuming the container has a lid that is made from the same material as the sides.Problem 18E:
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his bam. No...Problem 19E:
If the farmer in Exercise 18 wants to enclose 8000 square feet of land, what dimensions will...Problem 20E:
(a) Show that of all the rectangles with a given area, the one with smallest perimeter is a square....Problem 23E:
Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0).Problem 24E:
Find, correct to two decimal places, the coordinates of the point on the curve y = sin x that is...Problem 25E:
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r.Problem 26E:
Find the area of the largest rectangle that can be inscribed in the ellipse x2/a2 + y2/b2 = 1.Problem 27E:
Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral...Problem 28E:
Find the area of the largest trapezoid that can be inscribed in a circle of radius 1 and whose base...Problem 29E:
Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of...Problem 30E:
If the two equal sides of an isosceles triangle have length a, find the length of the third side...Problem 31E:
A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of...Problem 32E:
A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest...Problem 33E:
A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible surface...Problem 34E:
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the...Problem 35E:
The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area...Problem 36E:
A poster is to have an area of 180 in2 with 1-inch margins at the bottom and sides and a 2-inch...Problem 37E:
A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is...Problem 39E:
If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice...Problem 40E:
A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. What is...Problem 41E:
A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a...Problem 42E:
A cone-shaped paper drinking cup is to be made to hold 27 cm3 of water. Find the height and radius...Problem 43E:
A cone with height h is inscribed in a larger cone with height H so that its vertex is at the center...Problem 44E:
An object with weight W is dragged along a horizontal plane by a force acting along a rope attached...Problem 45E:
If a resistor of R ohms is connected across a battery of E volts with internal resistance r ohms,...Problem 46E:
For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is...Problem 47E:
In a beehive, each cell is a regular hexagonal prism, open at one end with a trihedral angle at the...Problem 48E:
A boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/h. Another boat has been...Problem 49E:
EXAMPLE 4 A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants...Problem 50E:
A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C...Problem 51E:
An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to...Problem 53E:
The illumination of an object by a light source is directly proportional to the strength of the...Problem 54E:
Find an equation of the line through the point (3, 5) that cuts off the least area from the first...Problem 57E:
What is the shortest possible length of the line segment that is cut off by the first quadrant and...Problem 58E:
What is the smallest possible area of the triangle that is cut off by the first quadrant and whose...Problem 60E:
(a) Show that if the profit P(x) is a maximum, then the marginal revenue equals the marginal cost....Problem 61E:
A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at 10, the...Problem 62E:
During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the...Problem 63E:
A retailer has been selling 1200 tablet computers a week at 350 each. The marketing department...Problem 64E:
A company operates 16 oil wells in a designated area. Each pump, on average, extracts 240 barrels of...Problem 65E:
Show that of all the isosceles triangles with a given perimeter, the one with the greatest area is...Problem 67E:
Consider the tangent line to the ellipse x2a2+y2b2=1 at a point (p, q) in the first quadrant. (a)...Problem 68E:
The frame for a kite is to be made from six pieces of wood. The four exterior pieces have been cut...Problem 69E:
A point P needs to be located somewhere on the line AD so that the total length L of cables linking...Problem 70E:
The graph shows the fuel consumption c of a car (measured in gallons per hour) as a function of the...Problem 71E:
Let v1 be the velocity of light in air and v2 the velocity of light in water. According to Fermats...Problem 72E:
Two vertical poles PQ and ST are secured by a rope PRS going from the top of the first pole to a...Problem 73E:
The upper right-hand corner of a piece of paper, 12 in. by 8 in., as in the figure, is folded over...Problem 74E:
A steel pipe is being carried down a hallway 9 ft wide. At the end of the hall there is a...Problem 75E:
An observer stands at a point P, one unit away from a track. Two runners start at the point S in the...Problem 76E:
A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the...Problem 77E:
Where should the point P be chosen on the line segment AB so as to maximize the angle ?Problem 78E:
A painting in an art gallery has height h and is hung so that its lower edge is a distance d above...Problem 79E:
Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length L...Problem 80E:
The blood vascular system consists of blood vessels (arteries, arterioles, capillaries, and veins)...Browse All Chapters of This Textbook
Chapter 1 - Functions And ModelsChapter 1.1 - Four Ways To Represent A FunctionChapter 1.2 - Mathematical Models: A Catalog Of Essential FunctionsChapter 1.3 - New Functions From Old FunctionsChapter 1.4 - Exponential FunctionsChapter 1.5 - Inverse Functions And LogarithmsChapter 2 - Limits And DerivativesChapter 2.1 - The Tangent And Velocity ProblemsChapter 2.2 - The Limit Of A FunctionChapter 2.3 - Calculating Limits Using The Limit Laws
Chapter 2.4 - The Precise Definition Of A LimitChapter 2.5 - ContinuityChapter 2.6 - Limits At Infinity; Horizontal AsymptotesChapter 2.7 - Derivatives And Rates Of ChangeChapter 2.8 - The Derivative As A FunctionChapter 3 - Differentiation RulesChapter 3.1 - Derivatives Of Polynomials And Exponential FunctionsChapter 3.2 - The Product And Quotient RulesChapter 3.3 - Derivatives Of Trigonometric FunctionsChapter 3.4 - The Chain RuleChapter 3.5 - Implicit DifferentiationChapter 3.6 - Derivatives Of Logarithmic FunctionsChapter 3.7 - Rates Of Change In The Natural And Social SciencesChapter 3.8 - Exponential Growth And DecayChapter 3.9 - Related RatesChapter 3.10 - Linear Approximations And DifferentialsChapter 3.11 - Hyperbolic FunctionsChapter 4 - Applications Of DifferentiationChapter 4.1 - Maximum And Minimum ValuesChapter 4.2 - The Mean Value TheoremChapter 4.3 - How Derivatives Affect The Shape Of A GraphChapter 4.4 - Indeterminate Forms And L'hospital's RuleChapter 4.5 - Summary Of Curve SketchingChapter 4.6 - Graphing With Calculus And CalculatorsChapter 4.7 - Optimization ProblemsChapter 4.8 - Newton's MethodChapter 4.9 - AntiderivativesChapter 5 - IntegralsChapter 5.1 - Areas And DistancesChapter 5.2 - The Definite IntegralChapter 5.3 - The Fundamental Theorem Of CalculusChapter 5.4 - Indefinite Integrals And The Net Change TheoremChapter 5.5 - The Substitution RuleChapter 6 - Applications Of IntegrationChapter 6.1 - Areas Between CurvesChapter 6.2 - VolumesChapter 6.3 - Volumes By Cylindrical ShellsChapter 6.4 - WorkChapter 6.5 - Average Value Of A FunctionChapter 7 - Techniques Of IntegrationChapter 7.1 - Integration By PartsChapter 7.2 - Trigonometric IntegralsChapter 7.3 - Trigonometric SubstitutionChapter 7.4 - Integration Of Rationai Functions By Partial FractionsChapter 7.5 - Strategy For IntegrationChapter 7.6 - Integration Using Tables And Computer Algebra SystemsChapter 7.7 - Approximate IntegrationChapter 7.8 - Improper IntegralsChapter 8 - Further Applications Of IntegrationChapter 8.1 - Arc LengthChapter 8.2 - Area Of A Surface Of RevolutionChapter 8.3 - Applications To Physics And EngineeringChapter 8.4 - Applications To Economics And BiologyChapter 8.5 - ProbabilityChapter 9 - Differential EquationsChapter 9.1 - Modeling With Differential EquationsChapter 9.2 - Direction Fields And Euler's MethodChapter 9.3 - Separable EquationsChapter 9.4 - Models For Population GrowthChapter 9.5 - Linear EquationsChapter 9.6 - Predator-prey SystemsChapter 10 - Parametric Equations And Polar CoordinatesChapter 10.1 - Curves Defined By Parametric EquationsChapter 10.2 - Calculus With Parametric CurvesChapter 10.3 - Polar CoordinatesChapter 10.4 - Areas And Lengths In Polar CoordinatesChapter 10.5 - Conic SectionsChapter 10.6 - Conic Sections In Polar CoordinatesChapter 11 - Infinite Sequences And SeriesChapter 11.1 - SequencesChapter 11.2 - SeriesChapter 11.3 - The Integral Test And Estimates Of SumsChapter 11.4 - The Comparison TestsChapter 11.5 - Alternating SeriesChapter 11.6 - Absolute Convergence And The Ratio And Root TestsChapter 11.7 - Strategy For Testing SeriesChapter 11.8 - Power SeriesChapter 11.9 - Representations Of Functions As Power SeriesChapter 11.10 - Taylor And Maclaurin SeriesChapter 11.11 - Applications Of Taylor PolynomialsChapter 12 - Vectors And The Geometry Of SpaceChapter 12.1 - Three-dimensional Coordinate SystemsChapter 12.2 - VectorsChapter 12.3 - The Dot ProductChapter 12.4 - The Cross ProductChapter 12.5 - Equations Of Lines And PlanesChapter 12.6 - Cylinders And Quadric SurfacesChapter 13 - Vector FunctionsChapter 13.1 - Vector Functions And Space CurvesChapter 13.2 - Derivatives And Integrals Of Vector FunctionsChapter 13.3 - Arc Length And CurvatureChapter 13.4 - Motion In Space: Velocity And AccelerationChapter 14 - Partial DerivativesChapter 14.1 - Functions Of Several VariablesChapter 14.2 - Limits And ContinuityChapter 14.3 - Partial DerivativesChapter 14.4 - Tangent Planes And Linear ApproximationsChapter 14.5 - The Chain RuleChapter 14.6 - Directional Derivatives And The Gradient VectorChapter 14.7 - Maximum And Minimum ValuesChapter 14.8 - Lagrange MultipliersChapter 15 - Multiple IntegralsChapter 15.1 - Double Integrals Over RectanglesChapter 15.2 - Double Integrals Over General RegionsChapter 15.3 - Double Integrals In Polar CoordinatesChapter 15.4 - Applications Of Double IntegralsChapter 15.5 - Surface AreaChapter 15.6 - Triple IntegralsChapter 15.7 - Triple Integrals In Cylindrical CoordinatesChapter 15.8 - Triple Integrals In Spherical CoordinatesChapter 15.9 - Change Of Variables In Multiple IntegralsChapter 16 - Vector CalculusChapter 16.1 - Vector FieldsChapter 16.2 - Line IntegralsChapter 16.3 - The Fundamental Theorem For Line IntegralsChapter 16.4 - Green's TheoremChapter 16.5 - Curl And DivergenceChapter 16.6 - Parametric Surfaces And Their AreasChapter 16.7 - Surface IntegralsChapter 16.8 - Stokes' TheoremChapter 16.9 - The Divergence TheoremChapter 17 - Second-order Differential EquationsChapter 17.1 - Second-order Linear EquationsChapter 17.2 - Nonhomogeneous Linear EquationsChapter 17.3 - Applications Of Second-order Differential EquationsChapter 17.4 - Series Solutions
Sample Solutions for this Textbook
We offer sample solutions for Calculus, Early Transcendentals, International Metric Edition homework problems. See examples below:
Chapter 1, Problem 1RCCChapter 2, Problem 1RCCChapter 3, Problem 1RCCChapter 4, Problem 1RCCChapter 5, Problem 1RCCChapter 6, Problem 1RCCChapter 7, Problem 1RCCChapter 8, Problem 1RCCChapter 9, Problem 1RCC
Chapter 10, Problem 1RCCChapter 11, Problem 1RCCChapter 12, Problem 1RCCVector function: The vector function is a function whose range is a set of vectors and whose domain...Chapter 14, Problem 1RCCGiven: The continuous function f is defined on a rectangle R=[a,b]×[c,d] . The double integral of f...Chapter 16, Problem 1RCCChapter 17, Problem 1RCC
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