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mathematics
mathematical applications for the management
Mathematical Applications For The Management, Life And Social Sciences 12th Edition Ronald J. Harshbarger, James J. Reynolds - Solutions
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 material, find x = f(t). Give your answer with 3 significant digit coefficients.(b) Use your answer from
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 function for this product?
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 50,000, what is the predicted population in the year 2028?
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) Find the average cost function.(b) Find the average cost of 20 units.
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) Find the average cost function.(b) Find the average cost of 12 units.
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 revenue for the product is MR = 80x, find the profit or loss from production and sale of(a) 3 units.(b) 8
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 fixed cost of $1000.(a) Find the profit or loss from the production and sale of 5 units.(b) How many
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 cost function and the cost of producing 20 units (to the nearest dollar).
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, find the total cost function and fixed costs.
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, find the total cost function.
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 cost function for the month.
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 and f"(x) < 0(d) f'(x) < 0 and f"(x) = 0 10 y = f(x) 8 В C 2 A + + + -2 4 6. 8 10 -2E F -4 2. 4,
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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