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mathematics
mathematical applications for the management

Questions and Answers of Mathematical Applications for the Management

If limx→5 [f(x) - g(x)] = 8 and limx→5 g(x) = 2, find(a) limx→5 f (x)(b) limx→5 {[g (x)]2 - f (x)}(c) limx→5 [2xg(x)/4 - f (x)]
If the profit function for a product is given byP(x) = 92x - x2 - 1760find limx→40 P(x).
If v(x) = 4/ 3√x, find v'(x).
If y = 1/x - 1/√x, find y'.
If f (x) = 3/2x2 - 3√x + 45, find f'(x).
The following table gives the total U.S. renewable electric power generation, in billions of kilowatt-hours, for selected years from 2012 and projected to 2040.(a) Model these data with a power
If p = 5q3/2q3 + 1, find dp/dq.
Find ds/dt if s = √t/(3t + 1).
Find dy/dx for y = √x (3x + 2).
The Hourly Parking Garage at BWI International Airport in Baltimore costs $2 per half hour during the first hour and $4 for each hour or part of an hour for more than 1 hour and up to 5 hours. If C =
Obesity (BMI ≥ 30) is a serious problem in the United States and is expected to get worse. Being overweight increases the risk of diabetes, heart disease, and many other ailments, but the severely
Obesity (BMI ≥ 30) is a serious problem in the United States and is expected to get worse. Being overweight increases the risk of diabetes, heart disease, and many other ailments, but the severely
Find dy/dx if y = x/3√3x - 1.
In Problems, find the fifth derivatives.y = (2x + 1)4
In Problems, find the fifth derivatives.y = (1 - x)6/24
In Problem, assume that a company’s monthly total revenue and total cost (both in dollars) are given byR(x) = 140x - 0.01x2 and C (x) = 60x + 70,000where x is the number of units. Let P(x) denote
In Problem, assume that a company’s monthly total revenue and total cost (both in dollars) are given byR(x) = 140x - 0.01x2 and C (x) = 60x + 70,000where x is the number of units. Let P(x) denote
In Problem, assume that a company’s monthly total revenue and total cost (both in dollars) are given byR(x) = 140x - 0.01x2 and C (x) = 60x + 70,000where x is the number of units. Let P(x) denote
The graph shows the revenue function for a commodity. Will the (A + 1)st item sold or the (B + 1)st item sold produce more revenue? Explain. R(x) + A + В Units Dollars
In Problem, cost, revenue, and profit are in dollars and x is the number of units.If the revenue function for a product isfind the marginal revenue. 60x R(x) 2х + 1
In Problem, complete the following.(a) Find the derivative of each function and evaluate it at the given x-value.(b) Use the numerical derivative feature of a graphing calculator to check your
In Problem, find the derivative of each function.z = 3t11/3 - 2t7/4 - t1/2 + 8
For each function in Problems, approximate f' (a) in the following ways.(a) Use f (a + h) - f (a)/h with h = 0.0001.(b) Graph the function on a graphing calculator. Then zoom in near the point until
Suppose that f (x) is a differentiable function. Use the table of values to approximate f'(3) as accurately as possible. 2 2.5 2.999 3 3.01 3.1 f(x) 18.4 44.896 45 46.05 56.18
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.s = [(4 - t2)(t2 + 5t)]4
In Problem, use properties of limits and algebraic methods to find the limits, if they exist.limx→-1/2 4x - 2/4x2 + 1
In Problem, find the indicated derivative.Find f(4)(x) if f (x) = 1/x.
Differentiate the functions in Problem. V2х - V2x – 1 - Vx X. y =
In Problem, find each limit, if it exists. [(x + h) – 2(x + h)*] – (x – 2x²) lim h 0 | h
In Problem, find the derivative of each function.y = x-1 - x-2 + 13
In Problem, suppose a company has its total cost for a product given by C(x) = 200x + 10,000 dollars and its total revenue given by R(x) = 250x - 0.01x2 dollars, where x is the number of units
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.p = [(q + 1)(q3 - 3)]3
In Problem, use properties of limits and algebraic methods to find the limits, if they exist.limx→-1/3 1 - 3x/9x2 + 1
In Problem, find the indicated derivative.Find f(4)(x) if f(x) = √x.
Differentiate the functions in Problem. (Зw + 1)' — 3w 7
In Problem, find each limit, if it exists. 3(x + h)? – 3x2 lim h
In Problem, find the derivative of each function.y = x-5 + x-8 - 3
In Problem, find the indicated derivatives and simplify. x(x + 4) y' for y = х — 2
In Problem, suppose a company has its total cost for a product given by C(x) = 200x + 10,000 dollars and its total revenue given by R(x) = 250x - 0.01x2 dollars, where x is the number of units
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.y = (x2 - 3)4/x
Suppose that the cost function for a commodity is C(x) = 300 + 6x + 0.05x2 dollars(a) Find the marginal cost at x = 8 units and tell what this predicts about the cost of producing 1 additional
Differentiate the functions in Problem. 5V1 - x y = .3 6 ||
In Problem, find each limit, if it exists. Sx - 2 - x2 if x< -2 lim f(x) where f(x) x-2 if x 2 -2
In Problem, at the indicated points, find(a) The slope of the tangent to the curve.(b) The instantaneous rate of change of the function.R(x) = 16x + x2, x = 1
For each function in Problem, find(a) The derivative using the definition.(b) The instantaneous rate of change of the function at any value and at the given value.(c) The slope of the tangent at the
In Problem, find the indicated derivatives and simplify. 2Vx - 1 dy for y dx 1 - 4V
Use the definition of continuity to investigate whether g(x) is continuous at x = -2. Show your work. [6 – - x if x < -2 if x>-2 g(x)
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.y = (x2 - 4)3/x2 + 1
In Problem, find the indicated derivative.Find d4y/dx4 if y = 4x3 - 16x.
Differentiate the functions in Problem. 11(x3 ソ= 7)6
In Problem, find each limit, if it exists. 4 - x2 if x 1 ||
In Problem, at the indicated points, find(a) The slope of the tangent to the curve.(b) The instantaneous rate of change of the function.P(x) = x3 - 6x, (2, -4)
For each function in Problem, find(a) The derivative using the definition.(b) The instantaneous rate of change of the function at any value and at the given value.(c) The slope of the tangent at the
In Problem, find the indicated derivatives and simplify. 31 dp for P 1- 9 aq
Use the given tables to evaluate the following limits, if they exist.(a) limx→5 f(x)(b) limx→5 g(x)(c) limx→5- g(x) 4.99 4.999 |→ 5+5.001 5.01 f(x) 2.01 2.001 →?+ 1.999 1.99 4.99
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.f (x) = (5x3 + 1)(x4 + 5x)2
In Problem, determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing each
In Problem, find the indicated derivative.If f (x) = √x - 5, find f"'(x).
In Problem, cost is in dollars and x is the number of units. Find the marginal cost functions for the given cost functions.C(x) = 50 + 48x + x3
Differentiate the functions in Problem.y = √x2 + 3x
In Problem, find each limit, if it exists. x2 - 8 lim x→2 x - 2
In Problem, find the indicated derivatives and simplify. dy 100x for y = 200x dx - Зх + 1
Find the average rate of change of f(x) = 4 - x - 2x2 over [1, 6].
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.y = (x - 1)2(x2 + 1)
In Problem, determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing each
In Problem, find the indicated derivative.If f (x) = √x + 1, find f"'(x).
In Problem, cost is in dollars and x is the number of units. Find the marginal cost functions for the given cost functions.C = 400 + 27x + x3
Differentiate the functions in Problem.y = √3x2 + 4x + 9
In Problem, find each limit, if it exists. x2 - 9 lim x→1 x - 3
In Problem, find the indicated derivatives and simplify. x² dz for z = x + dx || 1- x – 2x2 |
Let f(x) = x3 - 3x2 - 24x - 10.(a) Write the equation of the line tangent to the graph of y = f (x) at x = -1.(b) Find all points (both x- and y-coordinates) where f'(x) = 0.
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.y = 3x4(2x5 + 1)7
In Problem, complete each table and predict the limit, if it exists. S4 - x for x s-2 2 + 2x for x> -2 f(x) = lim f(x) = ? x-2 f(x) -2.1 -2.01 -2.001 - 1.999 -1.99
In Problem, determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing each
In Problem, find the indicated derivative.If y = x4 + x1/3, find d2y/dx2.
In Problem, cost is in dollars and x is the number of units. Find the marginal cost functions for the given cost functions.C = 0.1x3 - 1.5x2 + 9x + 15
Differentiate the functions in Problem. 1 y = (3x3 + 4х + 1)3/2
In Problem, find each limit, if it exists. x* — х — 12 lim X -3 2х - 6
Find the derivatives of the functions in Problem.h(x) = 12x20 + 8x10 - 2x7 + 17x - 9
In Problem, the tangent line to the graph of f (x) at x = 1 is shown. On the tangent line, P is the point of tangency and A is another point on the line.(a) Find the coordinates of the points P and
In Problem, find the indicated derivatives and simplify. - 4 3 - 2t? – t - 5 3 ds for s dt |
Find d3y/dx3 for y = x3 - x-3.
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.y = 5/3 x3 (4x5 - 5)3
In Problem, determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing each
In Problem, find the indicated derivative.If y = x5 - x1/2, find d2y/dx2.
In Problem, cost is in dollars and x is the number of units. Find the marginal cost functions for the given cost functions.C = x3 - 6x2 + 24x + 10
Differentiate the functions in Problem. 1 g(x) (2x3 + + 3x + 5)3/4
In Problem, find each limit, if it exists. x - 16 lim x→3 x - 3
Find the derivatives of the functions in Problem.g (x) = 2x12 - 5x6 + 9x4 - x - 5
In Problem, the tangent line to the graph of f (x) at x = 1 is shown. On the tangent line, P is the point of tangency and A is another point on the line.(a) Find the coordinates of the points P and
In Problem, find the indicated derivatives and simplify.dy/dx for y = 1 - 2x2/x4 - 2x2 + 5
In Problem, use derivative formulas to find the derivative of each function. Simplify, except for Problem 10.f (x) = 12√x - 10/x2 + 17
Find the derivatives of the functions in Problem. Simplify and express the answer using positive exponents only.y = 5/2 (3x4 - 6x2 + 2)5
In Problem, determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing each
In Problem, find the third derivative.y = 1/x2
Differentiate the functions in Problem. 1 8(t) 4t + 1
In Problem, find each limit, if it exists. 4 lim x- 6x + x - 1
Find the derivatives of the functions in Problem.u = 2t10 - 5t5 - 9
In Problem, find the indicated derivatives and simplify.C'(x) for C(x) = 2x3/3x4 + 2
In Problem, use derivative formulas to find the derivative of each function. Simplify, except for Problem 10.y = (x2 + 3)(2x + 5)6

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