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mathematics
mathematical applications for the management

Questions and Answers of Mathematical Applications for the Management

Use Table 13.2 in Section 13.5 to evaluate each of the following.(a) ∫ ln (2x) dx(b) ∫ x√3x - 7 dx
In Problem, evaluate the improper integrals that converge. 00 dt 1/3
In Problem, use integration by parts to evaluate the integral.∫ ln x/x2 dx
In Problem, use integration by parts to evaluate the integral. y(1 – y)}/2 - 9 dy
For each shaded region in Problem,(a) Form the integral that represents the area of the shaded region and(b) Find the area of the region. y = x3+1 2 x = 1 -2 y = -x – 1 2.
Evaluate the integrals in Problem. Identify the formula used.∫4(3x) dx
Evaluate the definite integrals in Problem. '5 x dx
A company that services a number of vending machines considers its income as a continuous stream with an annual rate of flow at time t given byf(t) = 120e-0.4tin thousands of dollars per year. Find
For each interval [a, b] and value of n given in Problems, find h and the values of x0, x1, . . . . . xn.[-1, 2] n = 6
If ∫41 f(x) dx = 3 and ∫43 f(x) dx = 7, find ∫31 2f(x) dx.
In Problem, evaluate the improper integrals that converge. 00 xe- dx
In Problem, use integration by parts to evaluate the integral. qVq – 4 dq 9.
Use integration by parts to evaluate the following.(a) ∫ 3xex dx(b) ∫ x ln (2x) dx
In Problem, use integration by parts to evaluate the integral.∫x3 ln x dx
Evaluate the following definite integrals. (Do not approximate with technology.)a.b.c.d.e.f. 4 (9 – 4x) dx
In Problem, use integration by parts to evaluate the integral.∫x2 ln x dx
Express the area in Quadrant I under y = 12 + 4x - x2 (shaded in the figure) as an integral. Then evaluate the integral to find the area. y 12 y = 12 + 4x – x² 6
In Problem, use integration by parts to evaluate the integral.∫xe-x dx
Use formulas to simplify 3i 3
Consider f(x) = 5 - 2x from x = 0 to x = 1 with n equal subdivisions.(a) If f (x) is evaluated at right-hand endpoints, find a formula for the sum, S, of the areas of the n rectangles.(b) Find
In Problem, use integration by parts to evaluate the integral.∫xe3x dx
Use left-hand endpoints and n = 4 subdivisions to approximate the area under f (x) = √4 - x2 on the interval [0, 2].
Suppose that the marginal propensity to save isdS/dy = 0.2 - 0.1e-2yand consumption is $7.8 billion when disposable income is $0. Find the national consumption function.
Evaluate the integrals in Problem. Check your results by differentiation.∫2(x3 - 1)(x4 - 4x + 3)-5 dx
Evaluate the integrals in Problem. Check your answers by differentiating.∫(2 + 2√x) dx
Suppose the supply function for a product is p = 40 + 0.001x2 and the demand function is p = 120 - 0.2x, where x is the number of units and p is the price in dollars. If the market equilibrium price
For selected years from 1985 and projected to 2035, the following table shows the U.S. energy use per dollar of GDP, viewed as a percent of the 1980 usage. Thus, in 2000, U.S. energy use per dollar
The following table shows the U.S. average annual wage in thousands of dollars for selected years from 2012 and projected to 2050. Suppose the rate of change of the U.S. average annual wage can be
The following table shows the number of U.S. non-farm employees N (in millions) for selected years from 2010 and projected to 2040. Suppose the rate of change of the number of these employees can be
Suppose the rate of change of the expected life span l at birth of people born in the United States can be modeled bywhere t is the number of years past 1920.(a) Use integration and the data point
National health expenditures per capita E (in dollars) have risen dramatically since 2000. By using data from the Centers for Medicare and Medicaid Services from 2002 and projected to 2024, the rate
The rate of disintegration of a radioactive substance can be described bywhere n0 is the number of radioactive atoms present when time t is 0, and K is a positive constant that depends on the
If national consumption is $8.5 billion when disposable income is $0 and if the marginal propensity to consume isdC/dy = 1/√2y + 16 + 0.6find the national consumption function.
In Problem, a family of functions is given and graphs of some members are shown. Find the function f(x) such that the family is given by ∫f(x) dx.F(x) = e0.4x + e-0.4x + C 14 12 10 -8-6-4 4 6 8 -4+
In Problem, a family of functions is given and graphs of some members are shown. Find the function f(x) such that the family is given by ∫f(x) dx.F(x) = 5xe-x + C y F(x) = 5xe-+C 10 -2 2 4 6.
In Problem, a family of functions is given and graphs of some members are shown. Find the function f(x) such that the family is given by ∫f(x) dx.F(x) = -ln (x2 + 4) + C y 10 5 - 10 10 -5- -10t to
In Problem, a family of functions is given and graphs of some members are shown. Find the function f(x) such that the family is given by ∫f(x) dx.F(x) = x + ln ІxІ + C 10 5 5 10 -10+ F(x) =
Evaluate the integrals in Problem. Check your results by differentiation. x + 1 dx Vx + 3x + 10
In Problem, find the particular solution to each differential equation.xey dx = (x + 1) dy when x = 0, y = 0
Evaluate the integrals in Problem. Check your results by differentiation. x2 - - 4x dx Vx - 6x + 2
In Problem, find the particular solution to each differential equation.2xy dy/dx = y2 + 1 when x = 1, y = 2
Evaluate the integrals in Problem. Check your results by differentiation. 3x – 2x (x6 – x4)5
In Problem, find the particular solution to each differential equation.y' = 1/xy when x = 1, y = 3
Evaluate the integrals in Problem. Check your results by differentiation. x - 1 (x* - 4x)3 dx
In Problem, find the particular solution to each differential equation.x2e2y dy = (x3 + 1) dx when x = 1, y = 0
In Problem, find the general solution to each differential equation.dy/dt = 4y/t
Evaluate the integrals in Problem. Check your results by differentiation. 5x dx (x* – 8)3
In Problem, find the particular solution to each differential equation.(x + 1) dy = y2dx when x = 0, y = 2
Evaluate the integrals in Problem. x* – 2x + x dx x2 – 2
In Problem, find the general solution to each differential equation.dy/dx = x/ey
Evaluate the integrals in Problem. Check your results by differentiation. 3x dx (2x – 5)*
Evaluate the integrals in Problem. ++ x + 3 dx x + 3
In Problem, find the general solution to each differential equation.t dy = dt/y + 1
Evaluate the integrals in Problem. Check your results by differentiation. ∫ 3√x2 + 2x (x + 1) dx
Evaluate the integrals in Problem. 2x + x + 2x + 3 dx 2x + 1
Evaluate the integrals in Problem. Check your results by differentiation. ∫√x3 - 3x (x2 - 1) dx
The following table gives the U.S. national consumption and disposable income (both in billions of dollars) for selected years from 2012 and projected to 2040. Suppose the marginal propensity to
Evaluate the integrals in Problem. x* - x + 1 dx x - 1
Evaluate the integrals in Problem. Check your answers by differentiating. 3x° + dx x, 4.
Evaluate the integrals in Problem. Check your results by differentiation.∫(2x4 + 3)2 (8x dx)
In Problem, find the general solution to the given differential equation.e4x(y + 1) dx + e2xy dy = 0
Evaluate the integrals in Problem. (x + 2) dx x² +4x – 9
Evaluate the integrals in Problem. Check your answers by differentiating. 2 dx Vx. 1
Evaluate the integrals in Problem. Check your results by differentiation. ∫(3x4 – 1)2 12xdx
In Problem, find the general solution to the given differential equation.(x2 + 2)ey2 dx = xydy
Suppose that the marginal propensity to save isand that consumption is $6 billion when disposable income is $0. Find the national consumption function. dS 1 0.2 dy V3y + 7
Evaluate the integrals in Problem. 2 + 1 dz 2 + 3z + 17
Evaluate the integrals in Problem. Check your answers by differentiating. 3 x' - 7 dx x*
Evaluate the integrals in Problem.a.b.c.d. 2х dx x² х — 1
Evaluate the integrals in Problem. Check your results by differentiation. ∫(x2 - 5)2 (2x2 dx)
In Problem, find the general solution to the given differential equation.x2y dy/dx = y2 + 1
Evaluate the integrals in Problem. 4x + 2x x* + x
Evaluate the integrals in Problem. Check your answers by differentiating. – 4 +· dx
Evaluate the integrals in Problem.(a) ∫(x2 - 1)4x dx(b) ∫(x2 - 1)10 x dx(c) ∫(x2 - 1)73x dx(d) ∫(x2 - 1)-2/3x dx
Evaluate the integrals in Problem. Check your results by differentiation.∫(x3 + 1)2 (3x dx)
In Problem, find the general solution to the given differential equation.(x + 1) dy/dx = y
Suppose that the marginal propensity to save isand that consumption is $12 billion when disposable income is $0. Find the national consumption function. dS 1 0.2 dy y + 1
Evaluate the integrals in Problem. 3x² dx 2x
Evaluate the integrals in Problem. Check your answers by differentiating. 2 dx 51 -3
Evaluate the integrals in Problem. 1 dx (х + 1)?
Evaluate the integrals in Problem. Check your results by differentiation.∫3x√5 - x2 dx
In Problem, find the general solution to the given differential equation.dy/dx = x2 + x/y + 1
Evaluate the integrals in Problem. 5x? Зx3 — 8
Evaluate the integrals in Problem. Check your answers by differentiating. dx -2
Evaluate the integrals in Problem. e2x 2 dx 2.
Evaluate the integrals in Problem. Check your results by differentiation.∫7x3√x4 + 6 dx
In Problem, find the general solution to the given differential equation.dy/dx = x/y
Suppose that the marginal propensity to save is dS/dy = 0.15 and that consumption is $5.15 billion when disposable income is $0. Find the national consumption function.
Evaluate the integrals in Problem. 4х dx 5x2 – 4
Evaluate the integrals in Problem. Check your answers by differentiating.∫6/x5 dx
Evaluate the integrals in Problem. 7x3 dx Vi – x*
Evaluate the integrals in Problem. Check your results by differentiation.∫3(x5 - 2x)(x6 - 6x2 + 7)-2 dx
In Problem, find the general solution to the given differential equation.y dx = x dy
Suppose that the marginal propensity to consume isand that consumption is $9.5 billion when disposable income is $0. Find the national consumption function. dC 0.6 – e-0.5y dy
Evaluate the integrals in Problem. 7x dx 4x – 9
Suppose that a liquid carries a drug with concentration 0.1 g/cc into a 160-cc organ at the rate of 4 cc/sec and leaves at the same rate. Find the amount of drug in the organ as a function of time t
Evaluate the integrals in Problem. Check your answers by differentiating.∫5/x4 dx
Evaluate the integrals in Problem. 6x7 dx (5x + 7)3
In Problem, find the general solution to the given differential equation.y2 dx = x dy
Evaluate the integrals in Problem. 6x3 dx 2x* + 1 4

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