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mathematics
mathematical applications for the management

Questions and Answers of Mathematical Applications for the Management

A certain radioactive material has a half-life of 100 days and the amount of material present, x, satisfiesdx/dt = kxwhere t is in days and k is constant.(a) If there are initially 100 g of this
Evaluate the integrals in Problem. Check your answers by differentiating.∫3 3√x2 dx
Evaluate the integrals in Problem.∫xe1+x2dx
Evaluate the integrals in Problem. Check your results by differentiation.∫(2x3 - x)(x4 - x2)6 dx
In Problem, find the general solution to the given differential equation.dy = (x2y3 + xy3) dx
Evaluate the integrals in Problem. dy y + 1
Suppose the marginal propensity to save is given byand national consumption is $6.6 billion when disposable income is $0. Find the national consumption function. dS 0.25 0.22 - dy V0.5y + 1 0.5у
Evaluate the integrals in Problem. Check your answers by differentiating.∫6 4√x dx
Evaluate the integrals in Problem.∫(x3 - e3x) dx
Evaluate the integrals in Problem. Check your results by differentiation.∫(x - 1)(x2 - 2x + 5)4 dx
In Problem, find the general solution to the given differential equation.dx = (x2y2 + x2)dy
Evaluate the integrals in Problem. dz 4z + 1
Suppose that the marginal cost for x units of a product is M̅C̅ = 4x + 50, the marginal revenue is M̅R̅ = 500, and the cost of the production and sale of 10 units is $1000. What is the profit
Evaluate the integrals in Problem. Check your answers by differentiating.∫(17 + √x3) dx
Evaluate the integrals in Problem.∫5 dx/e4x
Evaluate the integrals in Problem. Check your results by differentiation.∫5x3(3x4 + 7)-4 dx
If consumption is $6 billion when disposable income is $1 billion and if the marginal propensity to consume isfind the national consumption function. dC 0.3 0.4 + Vy dy
Evaluate the integrals in Problem. 8x7 to - 1
Suppose the rate of growth of the population of a city is predicted to bedp/dt = 2000t1.04where p is the population and t is the number of years past 2018. If the population in the year 2018 is
Evaluate the integrals in Problem. 3x2 2x – 7
Evaluate the integrals in Problem. Check your results by differentiation.∫8x5(4x6 + 15)-3 dx
If consumption is $8.7 billion when disposable income is $1 billion and if the marginal propensity to consume isfind the national consumption function. 0.2 0.3 + dC dy Vy
Evaluate the integrals in Problem. 3x dx х + 4 ах
Find the general solution of the separable differential equationdy/dx = x3y2.
Evaluate the integrals in Problem. Check your answers by differentiating. ∫(12x5 + 12x3 - 7) dx
Evaluate the integrals in Problem.∫(3x - 1)12 dx
Evaluate the integrals in Problem. Check your results by differentiation.∫3(5 - x)-3 dx
If national consumption is $9 billion when disposable income is $0 and if the marginal propensity to consume is 0.30, what is consumption when disposable income is $20 billion?
Evaluate the integrals in Problem. 5 dx e*/3 xe
In Problem, find the particular solution to each differential equation.dy/dx = e4x, if y(0) = 2
Evaluate the integrals in Problem. Check your answers by differentiating.∫(13 - 6x + 21x6) dx
Evaluate the integrals in Problem.∫y2ey3 dy
Evaluate the integrals in Problem. Check your results by differentiation.∫7(4x - 1)6 dx
Evaluate the integrals in Problem. 3 dx et/2 4x
In Problem, find the particular solution to each differential equation.y' = 4x3 + 3x2, if y(0) = 4
Evaluate the integrals in Problem. Check your answers by differentiating.∫(3x2 - 4x - 4) dx
Evaluate the integrals in Problem. Зх + 1 х — 1
Evaluate the integrals in Problem. Check your results by differentiation.∫9x5(3x6 - 4)6 dx
In Problem, find the particular solution.dy = (x2 - 1/x + 1) dx y(0) = 1/3
Evaluate the integrals in Problem.∫ x3/e4x4 dx
Find the general solution to f'(x) = x2/3 - 5/8.
Evaluate the integrals in Problem. Check your answers by differentiating.∫(x4 - 9x2 + 3) dx
Evaluate the integrals in Problem. + 1 dx a .2
Evaluate the integrals in Problem. Check your results by differentiation.∫4x3(7x4 + 12)3 dx
In Problem, find the particular solution.dy = (1/x - x) dx y(1) = 0
Evaluate the integrals in Problem.∫ x5/e2-3x6 dx
If ∫f (x) dx = 2x3 - x + 5ex + C, find f (x).
Evaluate the integrals in Problem. Check your answers by differentiating.∫(8 + x2/3) dx
Evaluate the integrals in Problem. Check your results by differentiation.∫(4x2 - 3x)4 (8x - 3) dx
Evaluate the integrals in Problem. dx (x'+1)²
In Problem, find the particular solution.y' = e2x+1 y(0) = e
In Problem, cost, revenue, and profit are in dollars and x is the number of units.The average cost of a product changes at the rate C̅'(x) = -10/x2 + 1/10 and the average cost of 10 units is $20.(a)
Evaluate the integrals in Problem.∫ 4/e1-2x dx
Evaluate ∫4x2/2x + 1 dx. Use long division.
Evaluate the integrals in Problem. Check your answers by differentiating.∫(3 - x3/2) dx
Evaluate the integrals in Problem.∫x2 dx/3√x3 - 4
Evaluate the integrals in Problem. Check your results by differentiation.∫(3x - x3)2 (3 - 3x2) dx
In Problem, find the particular solution.y' = e x-3 y(0) = 2
In Problem, cost, revenue, and profit are in dollars and x is the number of units.The average cost of a product changes at the rate C̅'(x) = -6x-2 + 1/6 and the average cost of 6 units is $10.(a)
Evaluate the integrals in Problem.∫ 3/e2x dx
Evaluate the integrals in Problem.∫5y3e2y4-1 dy
Evaluate the integrals in Problem. Check your answers by differentiating.∫(52 + x10) dx
Evaluate the integrals in Problem.∫x2/(x3 + 1)2 dx
In Problem, use integration to find the general solution to each differential equation.4y3 dy = (3x2 + 2x) dx
In Problem, cost, revenue, and profit are in dollars and x is the number of units.Suppose that the marginal cost for a product is M̅C̅ = 60√x + 1 and its fixed cost is $340. If the marginal
Evaluate the integrals in Problem.∫xe2x2dx
Evaluate the integrals in Problem.∫100e-0.01x dx
Evaluate the integrals in Problem.∫x2/x3 + 1 dx
In Problem, cost, revenue, and profit are in dollars and x is the number of units.Suppose that the marginal revenue for a product is MR = 900 and the marginal cost is M̅C̅ = 30√x + 4, with a
Evaluate the integrals in Problem. as 2s4 – 5
Evaluate the integrals in Problem.∫x3e3x4 dx
Evaluate the integrals in Problem. dx
Evaluate the integrals in Problem.∫5x2(3x3 + 7)6 dx
Evaluate the integrals in Problem.∫250e-0.5x dx
Evaluate the integrals in Problem.∫(3x2 - 6x + 1)-3(2x - 2) dx
Evaluate the integrals in Problem.∫(x3 + 4)23x dx
Evaluate the integrals in Problem.∫840e-0.7x dx
Evaluate the integrals in Problem.∫5x2(4x3 - 7)9 dx
Evaluate the integrals in Problem.∫(x3 - 3x2)5(x2 - 2x) dx
In Problem, cost, revenue, and profit are in dollars and x is the number of units.If the marginal cost for producing a product is M̅C̅ = 88 - 2e-0.01x, with a fixed cost of $6200, find the total
Evaluate the integrals in Problem.∫1600e0.4x dx
Evaluate the integrals in Problem.∫6x2(7 + 2x3)9dx
Evaluate the integrals in Problem.∫7x (x2 - 1)2 dx
In Problem, cost, revenue, and profit are in dollars and x is the number of units.If the marginal cost for a product is M̅C̅ = 140 + 0.15√x and the total cost of producing 100 units is $25,000,
Evaluate the integrals in Problem.∫1000e0.1x dx
Evaluate the integrals in Problem. 4 + Vx dx
In Problem, find the differential of each function.z = 4t - 4/t2
Evaluate the integrals in Problem.∫5(x2 - 1)dx
In Problem, find the differential of each function.p = 7q - 4q3/2
In Problem, cost, revenue, and profit are in dollars and x is the number of units.If the marginal cost for a product is M̅C̅ = 4x + 2 and the production of 10 units results in a total cost of $300,
Evaluate the integrals in Problem.∫(11 - 2x3)dx
In Problem, find the differential of each function.u = 3x4 - 4x3
In Problem, cost, revenue, and profit are in dollars and x is the number of units.If the monthly marginal cost for a product is M̅C̅ = x + 30 and the related fixed costs are $5000, find the total
Evaluate the integrals in Problem.∫(6x2 + 8x - 7) dx
In Problem, find the differential of each function.u = 2x5 + 9
In Problem, use the graph shown in the figure and identify points from A through I that satisfy the given conditions.(a) f'(x) > 0 and f"(x) < 0(b) f'(x) < 0 and f"(x) > 0(c) f'(x) = 0
Find the derivatives of the functions in Problem. y = 1 – 2e
If x2 + 3x2y4 = y + 8, find dy/dx.
Find dy/dx if y = ln (3x + 2/x2 - 5)1/4.
Find the derivatives of the functions in Problem.y = ln (e4x + 2)

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