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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 5 through 18, sketch the given region R and then find its area.R is the trapezoid bounded by the lines y = x + 6 and x = 2 and the coordinate axes.
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. 1 3t* dt 4 -1
A national consumers’ association has compiled statistics suggesting that the fraction of its members who are still active t months after joining is given by f(t) = e−0.2t. A new local chapter has 200 charter members and expects to attract new members at the rate of 10 per month. How many
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. x² + 2x + 1 x² dx
In Exercises 5 through 18, sketch the given region R and then find its area.R is the trapezoid bounded by the lines y = x + 2, y = 8 − x, x = 2, and the y axis.
It is estimated that t weeks from now, contributions in response to a fundraising campaign will be coming in at the rate of R'(t) = 5,000e−0.2t dollars per week, while campaign expenses are expected to accumulate at the constant rate of $676 per week.a. For how many weeks does the rate of revenue
In Exercises 1 through 20, find the indicated indefinite integral. Vln x [(VIT) dx
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. 4 S₁2v 2√u du
Sarah Greene is running for mayor. Polls indicate that the fraction of those who support her t weeks after first learning of her candidacy is given by f(t) = e−0.03t. At the time she declared her candidacy, 25,000 people supported her, and new converts are being added at the constant rate of 100
In Exercises 1 through 20, find the indicated indefinite integral. et [(₁ + et + 5, dx
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. 3 10x³ 5x √x²-x² +6 4 dx
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. x² + 3x - 2 Vx dx
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. [₁124¹/3 -1 (2u¹/3 - ²/3) du
In Exercises 19 through 24, find the average value of the given function f (x) over the specified interval a ≤ x ≤ b.f(x) = 1 − x2 over −3 ≤ x ≤ 3
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. Зи - 3 (u² - 2u + 6)² du
Suppose that when it is t years old, a particular industrial machine generates revenue at the rate R'(t) = 6,025 – 8t2 dollars per year, while operating and maintenance costs accumulate at the rate C'(t) = 4,681 + 13t2 dollars per year.a. The useful life of a machine is the number of years T
A certain nuclear power plant produces radioactive waste in the form of strontium-90 at the constant rate of 500 pounds per year. The waste decays exponentially with a half-life of 28 years. How much of the radioactive waste from the nuclear plant will be present after 140 years?
In Exercises 21 through 30, evaluate the indicated definite integral. Some (5x4 - 8x³ + 1) dx
A new strain of influenza has just been declared an epidemic by health officials. Currently, 5,000 people have the disease and 60 more victims are added each day. If the fraction of infected people who still have the disease t days after contracting it is given by f(t) = e−0.02t, how many people
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. fa³-2 3 (1-5) dx - 21²
In Exercises 19 through 24, find the average value of the given function f (x) over the specified interval a ≤ x ≤ b.f(x) = x2 − 3x + 5 over −1 ≤ x ≤ 2
Answer the questions in Exercise 20 for a machine that generates revenue at the rate R'(t) = 7,250 − 18t2 dollars per year and for which costs accumulate at the rate C'(t) = 3,620 + 12t2 dollars per year.Data from Exercises 20Suppose that when it is t years old, a particular industrial machine
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. (9 [₁₁ X 4 -3/2 dx
In Exercises 21 through 30, evaluate the indicated definite integral. ¹P (z/e-4 + 1/^) t.
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. Sex(4- 10 e *(4- e¹) dx
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. [x²(2y + 1) d dy
In Exercises 19 through 24, find the average value of the given function f (x) over the specified interval a ≤ x ≤ b.f(x) = e−x(4 − e2x) over −1 ≤ x ≤ 1
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. [Vic². √t(t² − 1) dt
In Exercises 19 through 24, find the average value of the given function f (x) over the specified interval a ≤ x ≤ b. f(x) et - é e et + ex -X over 0≤x≤ In 3
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. In 5x X - dx
The government of a small country estimates that the demand for oil is increasing exponentially at the rate of 10% per year. If the demand is currently 30 billion barrels per year, how much oil will be consumed in this country during the next 10 years?
In Exercises 19 through 24, find the average value of the given function f (x) over the specified interval a ≤ x ≤ b.f(x) = e2x + e−x over 0 ≤ x ≤ ln 2
The administrators of a town estimate that the fraction of people who will still be residing in the town t years after they arrive is given by the function f (t) = e−0.04t. If the current population is 20,000 people and new townspeople arrive at the rate of 500 per year, what will be the
In Exercises 21 through 30, evaluate the indicated definite integral. fore²e (e²x + 4√√x) dx
Answer the questions in Exercise 22 for a charity campaign in which contributions are made at the rate of R'(t) = 6,537e−0.3t dollars per week and expenses accumulate at the constant rate of $593 per week.Data from Exercises 22It is estimated that t weeks from now, contributions in response to a
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. fx(2 x(2x + 1)² dx
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. L ( 1 - - 1 - ) d x dx e
In Exercises 19 through 24, find the average value of the given function f (x) over the specified interval a ≤ x ≤ b. x + 1 x² + 2x + 6 over 1 ≤ x ≤ 1
In Exercises 21 through 30, evaluate the indicated definite integral. 2x² + √x - 5 X dx
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. 1 √xmx² x ln x - dx
The operators of a new computer dating service estimate that the fraction of people who will retain their membership in the service for at least t months is given by the function f(t) = e−t/10. There are 8,000 charter members, and the operators expect to attract 200 new members per month. How
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. L'₁x² + (x² + 3x³ + 1) dx
In Exercises 21 through 30, evaluate the indicated definite integral. -1 30(5x - 2)² dx
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. 1 x(In x)² dx
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. [ce (e¹ + 1)² dt
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. 1 - dx x ln x
Money is transferred continuously into an account at the constant rate of $2,400 per year. The account earns interest at the annual rate of 6% compounded continuously. How much will be in the account at the end of 5 years?
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. L₁ (-3.6² (-3x³ 3x² + 2x + 5) dx
In Exercises 21 through 30, evaluate the indicated definite integral. [ (3x + 6) 1(x + 4x + 5)? dx
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. 2x In(x² + 1) x² + 1 dx
In Exercises 25 through 28, find the average value V of the given function over the specified interval. In each case, sketch the graph of the function along with the rectangle whose base is the given interval and whose height is the average value V.f(x) = 2x − x2 over 0 ≤ x ≤ 2
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. Je -0.02-0.13t (e + 4) dt
Magda wants to expand and renovate her import store and is presented with two plans for making the improvements. The first plan will cost her $40,000, and the second will cost only $25,000. However, she expects the improvements resulting from the first plan to provide income at the continuous rate
Calculate the rate (in cubic centimeters per second) at which blood flows through an artery of radius 0.1 centimeter if the speed of the blood r centimeters from the central axis is 8 − 800r2 centimeters per second.
In Exercises 25 through 28, find the average value V of the given function over the specified interval. In each case, sketch the graph of the function along with the rectangle whose base is the given interval and whose height is the average value V. h(u) = U over 2 ≤ u 4 ≤
The population density r miles from the center of a certain city is D(r) = 5,000(1 + 0.5r2)−1 people per square mile.a. How many people live within 5 miles of the city center?b. The city limits are set at a radius L where the population density is 1,000 people per square mile. What is L, and what
Money is transferred continuously into an account at the constant rate of $1,000 per year. The account earns interest at the annual rate of 10% compounded continuously. How much will be in the account at the end of 10 years?
Blood flows through an artery of radius R. At a distance r centimeters from the central axis of the artery, the speed of the blood is given by S(r) = k(R2 − r2). Show that the average velocity of the blood is one-half the maximum speed.
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. 5 Ixy+eva) ay dy Зу
In Exercises 25 through 28, find the average value V of the given function over the specified interval. In each case, sketch the graph of the function along with the rectangle whose base is the given interval and whose height is the average value V.f(x) = x over 0 ≤ x ≤ 4
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. ¹P (² + - !^~^) J
At age 25, Tim starts making annual deposits of $2,500 into an IRA account that pays interest at an annual rate of 5% compounded continuously. Assuming that his payments are made as a continuous income flow, how much money will be in his account if he retires at age 60? At age 65?
In Exercises 21 through 30, evaluate the indicated definite integral. Jo 2te²2²-1 dt
The population density r miles from the center of a certain city is D(r) = 25,000e−0.05r2 people per square mile. How many people live between 1 and 2 miles from the city center?
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. Vx е feve X dx
In Exercises 21 through 30, evaluate the indicated definite integral. x ["" ( + + 1) dx
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. e *(1 + e²¹) dx
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. f=/=(x + X -(x + 1)² dx
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. 1 S² ( ₁ + ² + + + + 7) ₁² 1 dx X X
In Exercises 21 through 30, evaluate the indicated definite integral. 10 e¯*(ex + 1)¹/² dx
Fat travels through the bloodstream attached to protein in a combination called a lipoprotein. Low-density lipoprotein (LDL) picks up cholesterol from the liver and delivers it to the cells, dropping off any excess cholesterol on the artery walls. Too much LDL in the bloodstream increases the risk
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. et + e et - é e -x dx
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. t-1/2(²-t + 2) dt
In Exercises 25 through 28, find the average value V of the given function over the specified interval. In each case, sketch the graph of the function along with the rectangle whose base is the given interval and whose height is the average value V.g(t) = e−2t over −1 ≤ t ≤ 2
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. In 2 (e² - e¹) dt
In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. In(e) dx
An investment will generate income continuously at the constant rate of $1,200 per year for 5 years. If the prevailing annual interest rate remains fixed at 5% compounded continuously, what is the present value of the investment?
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. 14 -3 ¹t+1 1³ dt
In Exercises 21 through 30, evaluate the indicated definite integral. [² 1 x(ln x)² 2 dx
In Exercises 29 through 34, find the Gini index for the given Lorenz curve.L(x) = x3
The management of a national chain of fast-food outlets is selling a 10-year franchise in Cleveland, Ohio. Past experience in similar localities suggests that t years from now the franchise will be generating profit at the rate of f(t) = 100,000 dollars per year. If the prevailing annual interest
A group has just been formed with an initial membership of 10,000. Suppose that the fraction of the membership of the group that remain members for at least t years after joining is S(t) = e−0.03t, and that at time t, new members are being added at the rate of R(t) = 10e0.017t members per year.
In Exercises 29 through 34, find the Gini index for the given Lorenz curve.L(x) = x2
Felipe is trying to choose between two investment opportunities. The first will cost $50,000 and is expected to produce income at the continuous rate of $15,000 per year. The second will cost $30,000 and is expected to produce income at the rate of $9,000 per year. If the prevailing rate of
In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. x²(x - 1) dx
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. S - 1 t + 1 - dt
Repeat Exercise 34 for another drug for which the infection rate isAssume the government comparison rate stays the same; that is,Data from Exercises 34A pharmaceutical firm has been granted permission by the FDA to test the effectiveness of a new drug in combating a virus. The firm administers the
In Exercises 31 through 38, sketch the indicated region R and find its area by integration.R is the region under the curve y = x + 2√x over the interval 1≤ x ≤ 4.
In Exercises 29 through 34, find the Gini index for the given Lorenz curve.L(x) = 0.55x2 + 0.45x
Kevin spends $4,000 for an investment that generates a continuous income stream at the rate of f1(t) = 3,000 dollars per year. His friend, Molly, makes a separate investment that also generates income continuously, but at a rate of f2(t) = 2,000e0.04t dollars per year. The couple discovers that
In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. xV2x + 1 dx
In Exercises 31 through 34, solve the given initial value problem for y = f(x).dy/dx = 3x − 2 where y = 2 when x −1
In Exercises 29 through 34, find the Gini index for the given Lorenz curve. L(x) - 2 ابن 3.7 + -x 3
In Exercises 31 through 34, solve the given initial value problem for y = f(x). dy 2 dx X 1 2 X where y = -1 when x = 1
Repeat Exercise 33 for C(q) = 2q3 − 59q2 + 4q + 7,600 and p = 124 − 2q.Data from Exercises 33A manufacturer of machinery parts determines that q units of a particular piece will be sold when the price is p = 110 − q dollars per unit. The total cost of producing those q units is C(q) dollars,
A manufacturer of machinery parts determines that q units of a particular piece will be sold when the price is p = 110 − q dollars per unit. The total cost of producing those q units is C(q) dollars, wherea. How much profit is derived from the sale of the q units at p dollars per unit?b. For what
Answer the question in Exercise 32 for a constant renewal rate R = 1,000 and the survival functionData from Exercises 32The population of a small town is currently 85,000. A study commissioned by the mayor’s office finds that people are settling in the town at the rate of R(t) = 1,200e0.01t per
In Exercises 29 through 34, find the Gini index for the given Lorenz curve.L(x) = 0.7x2 + 0.3x
In Exercises 31 through 38, sketch the indicated region R and find its area by integration.R is the region under the curveover the interval 0 ≤ x ≤ 1. y = √9 - 5x² V9
In Exercises 31 through 38, sketch the indicated region R and find its area by integration.R is the region under the curve y = ex + e−x over the interval −1 ≤ x ≤ 1.
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