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mathematics
calculus with applications
Calculus For Business, Economics And The Social And Life Sciences 11th Brief Edition Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price - Solutions
In Exercises 13 through 20, find the slope and intercepts of the line whose equation is given and sketch the graph of the line.5y − 3x = 4
In Exercises 17 through 28, decide if the given function is continuous at the specified value of x.f(x) = x3 − 2x2 + x − 5 at x = 0
In Exercises 7 through 26, find the indicated limit if it exists. x + 3 lim x-55-x
In Exercises 13 through 20, find the slope and intercepts of the line whose equation is given and sketch the graph of the line.3x + 2y = 6
In Exercises 9 through 12, find the slope and intercepts of the line shown. Then find an equation for the line. ++ X
In Exercises 17 through 28, decide if the given function is continuous at the specified value of x.f(x) = 5x2 − 6x + 1 at x = 2
In Exercises 5 through 16, find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or −∞. lim x-5+ V2x - 1-3 x-5
In Exercises 5 through 16, find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or −∞. √x+1-2 lim x-3+ x-3
In Exercises 7 through 26, find the indicated limit if it exists. 2x + 3 lim x1 x + 1
In Exercises 7 through 26, find the indicated limit if it exists. x + 1 lim x 1/3 x + 2
In Exercises 13 through 20, find the slope and intercepts of the line whose equation is given and sketch the graph of the line.y = 3x − 6
In Exercises 5 through 16, find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or −∞. x - √x Vx lim x x - 1
A truck is hired to transport goods from a factory to a warehouse. The driver’s wages are figured by the hour and so are inversely proportional to the speed at which the truck is driven. The cost of gasoline is directly proportional to the speed. Express the total cost of operating the truck as a
In Exercises 7 through 26, find the indicated limit if it exists. lim (x²+1)(1 - 2x)² x->-1
In Exercises 13 through 20, find the slope and intercepts of the line whose equation is given and sketch the graph of the line.y = 3x
In Exercises 9 through 12, find the slope and intercepts of the line shown. Then find an equation for the line. * ++ x
At a certain factory, setup cost is directly proportional to the number of machines used and operating cost is inversely proportional to the number of machines used. Express the total cost as a function of the number of machines used.
In Exercises 5 through 16, find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or −∞. x² + 4 lim x-2 X-2
In Exercises 13 through 20, find the slope and intercepts of the line whose equation is given and sketch the graph of the line.y = 5
In Exercises 7 through 26, find the indicated limit if it exists. lim (x - 1)²(x + 1) x-3
The population (in thousands) of a colony of bacteria t minutes after the introduction of a toxin is given by the functiona. When does the colony die out?b. Explain why the population must be 10,000 some time between t = 1 and t = 7. f(t) = S²² +7 -8t + 72 ift≥ 5 if 0 ≤ t < 5
In Exercises 9 through 12, find the slope and intercepts of the line shown. Then find an equation for the line. H y
In Exercises 5 through 16, find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or −∞. lim (x - √x) x-0
In Exercises 13 through 20, find the slope and intercepts of the line whose equation is given and sketch the graph of the line.x = 3
Suppose it is known that producers will supply x units of a certain commodity to the market when the price is p = S(x) dollars per unit and that the same number of units will be demanded (bought) by consumers when the price is p = D(x) dollars per unit, wherefor constants A and B. It is also known
The rate at which people are implicated in a government scandal is jointly proportional to the number of people already implicated and the number of people involved who have not yet been implicated. Express this rate as a function of the number of people who have been implicated.
In Exercises 7 through 26, find the indicated limit if it exists. lim (1 - 5x¹) x-1/2
Find each of these limits. If the limit is infinite, indicate whether it is +∞ or −∞. a. lim x→-1 b. lim x-1 c. lim x-1 x² + 2x - 3 x 1 d. lim x² + 2x - 3 x-1 x² - x - 1 - - x 2 2x³ + 3x - 5 x+∞ x² + 2x + 7
In a study of mutation in fruit flies, researchers radiate flies with X-rays and determine that the mutation percentage M increases linearly with the X-ray dosage D, measured in kilo-Roentgens (kR). When a dose of D = 3 kR is used, the percentage of mutations is 7.7%, while a dose of 5 kR results
The rate at which an epidemic spreads through a community is jointly proportional to the number of people who have caught the disease and the number who have not. Express this rate as a function of the number of people who have caught the disease.
In Exercises 1 through 4, find the one-sided limitsfrom the given graph of f and determine whether lim f(x) and lim f(x)_ x→2 x2+
In Exercises 5 through 16, find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or −∞. lim x 2 x + 3 x + 2
In Exercises 7 through 26, find the indicated limit if it exists. lim (x²³ - 2x² + x − 3) - x--1
In Exercises 7 through 26, find the indicated limit if it exists. lim (x² - 6x + 7) x-0
In Exercises 5 through 16, find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or −∞. lim V4 - 2x x→2
The rate at which the temperature of an object changes is proportional to the difference between its own temperature and the temperature of the surrounding medium. Express this rate as a function of the temperature of the object.
In Exercises 9 through 12, find the slope and intercepts of the line shown. Then find an equation for the line. ►x
In Exercises 1 through 8, find the slope (if defined) of the line that passes through the given pair of points. 5 and 1 (+5) 11
A closed box with a square base has a surface area of 4,000 square centimeters. Express its volume as a function of the length of its base.
In Exercises 7 through 26, find the indicated limit if it exists. lim (3x²5x + 2) x-2
In Exercises 5 through 16, find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or −∞. lim V3x - 9 x-3+
In Exercises 5 through 16, find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or −∞. lim x(2-x)
In Exercises 1 through 4, find the one-sided limitsfrom the given graph of f and determine whether lim f(x) and lim f(x)_ x→2 x2+
A sample of radium decays at a rate proportional to the amount of radium remaining. Express the rate of decay of the sample as a function of the amount remaining.
In Exercises 1 through 6, find if it exists. lim f(x) a
In Exercises 1 through 6, find if it exists. lim f(x) a
In Exercises 1 through 8, find the slope (if defined) of the line that passes through the given pair of points. 2 3' 5 and 1 7' 8,
A closed box with a square base is to have a volume of 1,500 cubic inches. Express its surface area as a function of the length of its base.
In Exercises 1 through 4, find the one-sided limitsfrom the given graph of f and determine whether lim f(x) and lim f(x)_ x→2 x2+
In Exercises 1 through 6, find if it exists. lim f(x) a
In Exercises 1 through 8, find the slope (if defined) of the line that passes through the given pair of points.(−1.1, 3.5) and (−1.1, −9)
A city recreation department plans to build a rectangular playground 3,600 square meters in area. The playground is to be surrounded by a fence. Express the length of the fencing as a function of the length of one of the sides of the playground, draw the graph, and estimate the dimensions of the
In Exercises 5 through 16, find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +∞ or −∞. lim (3x² - 9)
Express the area of a rectangular field whose perimeter is 320 meters as a function of the length of one of its sides. Draw the graph, and estimate the dimensions of the field of maximum area.
Sketch the graph of each of these functions. Be sure to show all intercepts and any high or low points.a. f(x) = 3x − 5 b. f(x) = −x2 + 3x + 4
In Exercises 1 through 4, find the one-sided limitsfrom the given graph of f and determine whether lim f(x) and lim f(x)_ x→2 x2+
In Exercises 1 through 6, find if it exists. lim f(x) a
In Exercises 1 through 6, find if it exists. lim f(x) a
Find the composite function g(h(x)), where g(u) 1 2u + 1 and h(x) = x + 2 2x + 1
In Exercises 1 through 8, find the slope (if defined) of the line that passes through the given pair of points.(2, 6) and (2, −4)
A farmer wishes to fence off a rectangular field with 1,000 feet of fencing. If the long side of the field is along a stream (and does not require fencing), express the area of the field as a function of its width.
Specify the domain of the function f(x) = 2x - 1 V4-x²
In Exercises 1 through 8, find the slope (if defined) of the line that passes through the given pair of points.(5, −1) and (−2, −1)
A landscaper wishes to make a rectangular flower garden that is twice as long as it is wide. Express the area of the garden as a function of its width.
Find an equation for each of these lines:a. Through the point (−1, 2) with slope −1/2.b. With slope 2 and y intercept −3
In Exercises 1 through 8, find the slope (if defined) of the line that passes through the given pair of points.(2, 0) and (0, 2)
In the absence of environmental constraints, population grows at a rate proportional to its size. Express the rate of population growth as a function of the size of the population.
The product of two numbers is 318. Express the sum of the numbers as a function of the smaller number.
In Exercises 1 through 8, find the slope (if defined) of the line that passes through the given pair of points.(−1, 2) and (2, 5)
The sum of two numbers is 18. Express the product of the numbers as a function of the smaller number.
In Exercises 1 through 8, find the slope (if defined) of the line that passes through the given pair of points.(2, −3) and (0, 4)
In Exercises 1 through 6, find if it exists. lim f(x) a
In Exercises 21 through 36, write an equation for the line with the given properties.Through (0, 0) with slope 5
In Exercises 17 through 28, decide if the given function is continuous at the specified value of x. f(x) = Vx √x - 2 x - 4 at x = 2
A company makes two products, A and B. The manager estimates that if x% of the total marketing budget is spent on marketing product A, then the total profit gained from both products will be P thousand dollars, wherea. Sketch the graph of P(x).b. What is the company’s profit when the marketing
In Exercises 7 through 26, find the indicated limit if it exists. lim x² + 4x - 5 x-1
In Exercises 17 through 28, decide if the given function is continuous at the specified value of x. f(x) = √x - 2 x - 4 at x = 4
In Exercises 7 through 26, find the indicated limit if it exists. 2 9-x-zx lim x2x² + 3x + 2
Usually, when you purchase a lot in an auction, you pay not only your winning bid price but also a buyer’s premium. At one auction house, the buyer’s premium is 17.5% of the winning bid price for purchases up to $50,000. For larger purchases, the buyer’s premium is 17.5% of the first $50,000
Farmers can get $8 per bushel for their potatoes on July 1, and after that, the price drops by 5 cents per bushel per day. On July 1, a farmer has 140 bushels of potatoes in the field and estimates that the crop is increasing at the rate of 1 bushel per day. Express the farmer’s revenue from the
In Exercises 21 through 36, write an equation for the line with the given properties.Through (5, −2) with slope −1/2
If $1,000 is invested at 5% compounded n times per year, the balance after 1 year will be 1,000(1 + 0.05x)1/x, where x = 1/n is the length of the compounding period. For example, if n = 4, the compounding period is 1/4 year long. When the length of the compounding period approaches zero, we say
A closed box with a square base is to have a volume of 250 cubic meters. The material for the top and bottom of the box costs $2 per square meter, and the material for the sides costs $1 per square meter. Express the construction cost of the box as a function of the length of its base.
In Exercises 17 through 28, decide if the given function is continuous at the specified value of x. f(x) = [x+1 ifx≤2 12 if x > 2 at x = 2
In Exercises 17 through 28, decide if the given function is continuous at the specified value of x. f(x) Jx+1 x-1 if x < 0 if x ≥ 0 at x = 0
In Exercises 7 through 26, find the indicated limit if it exists. lim x 4 √x - 2 x - 4
In Exercises 7 through 26, find the indicated limit if it exists. lim x 9 √x - 3 x 9
A bus company has adopted the following pricing policy for groups that wish to charter its buses. Groups containing no more than 40 people will be charged a fixed amount of $2,400 (40 times $60). In groups containing between 40 and 80 people, everyone will pay $60 minus 50 cents for each person in
A local natural history museum charges admission to groups according to the following policy. Groups of fewer than 50 people are charged a rate of $3.50 per person, while groups of 50 people or more are charged a reduced rate of $3 per person.a. Express the amount a group will be charged for
For Exercises 27 through 36, findandIf the limiting value is infinite, indicate whether it is +∞ or −∞.f(x) = x3 − 4x2 − 4 X lim f(x) 00
In Exercises 17 through 28, decide if the given function is continuous at the specified value of x. f(x) = [x² + 1 if x ≤ 3 2x + 4 if x > 3 at x = 3
In Exercises 17 through 28, decide if the given function is continuous at the specified value of x. f(x) = [x²2² - 1 x + 1 ₁²-3 if x < -1 if x ≥ −1 at x = -1
In Exercises 21 through 36, write an equation for the line with the given properties.Through (2, 5) and parallel to the x axis
Ahmad must decide between two publishers who are vying for his new book. Publisher A offers royalties of 1% of net proceeds on the first 30,000 copies and 3.5% on all copies in excess of that figure, and expects to net $2 on each copy sold. Publisher B will pay no royalties on the first 4,000
For Exercises 27 through 36, findandIf the limiting value is infinite, indicate whether it is +∞ or −∞.f(x) = 1 − x + 2x2 − 3x3 X lim f(x) 00
In Exercises 21 through 36, write an equation for the line with the given properties.Through (2, 5) and parallel to the y axis
The charge for maintaining a checking account at a certain bank is $12 per month plus 10 cents for each check that is written. A competing bank charges $10 per month plus 14 cents per check. Find a criterion for deciding which bank offers the better deal.
In Exercises 21 through 36, write an equation for the line with the given properties.Through (1, 0) and (0, 1)
In Exercises 21 through 36, write an equation for the line with the given properties.Through (2, 5) and (1, −2)
For Exercises 27 through 36, findandIf the limiting value is infinite, indicate whether it is +∞ or −∞.f(x) = (1 − 2x)(x + 5) X lim f(x) 00
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