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college mathematics for business

Questions and Answers of College Mathematics For Business

In Problem find the family of all antiderivatives of each derivative. dx 7t dt f (r + 5)6
Suppose that the inventory of a certain item t months after the first of the year is given approximately byI(t) = 10 + 36t - 3t2 0 ≤ t ≤ 12What is the average inventory for the second quarter of
In Problem find the family of all antiderivatives of each derivative. dm 10n(n – 8)7 dn
In Problems find the derivative or indefinite integral as indicated. d. (4х? — Зх + 5) dx dx
Given the price–supply functionp = S(x) = 8(e0.05x - 1)find the average price (in dollars) over the supply interval [40, 50].
In Problem find the family of all antiderivatives of each derivative. dy 3t dt Vr - 4
A company producing electric motors has established that, on the average, a new employee can assemble N(t) components per day after t days of on-the-job training, as shown in the following table (a
In Problems find the derivative or indefinite integral as indicated. d 2 - In t dt - dt dt 3t + 2
In Problem find the family of all antiderivatives of each derivative. dy 5x? (x³ – 7)4 dx
Show that the rate of logistic growth, dy/dt = ky(M - y), has its maximum value when y = M/2.
In Problems find the derivative or indefinite integral as indicated. d (e2-7 + 1) dt dt
The market research department for an automobile company estimates that sales (in millions of dollars) of a new electric car will increase at the monthly rate ofS′(t) = 4e-0.08t 0 ≤ t ≤ 24t
In Problem find the family of all antiderivatives of each derivative. dp et + e* dx (e - e)2
The rate of healing, A′(t) (in square centimeters per day), for a certain type of skin wound is given approximately by the following table:(A) Use left and right sums over five equal subintervals
Use differentiation to justify the formulaprovided that n ≠ -1. + C n + 1 x" dr
The area of a healing skin wound changes at a rate given approximately bywhere t is time in days and A(1) = 5 square centimeters. What will be the area of the wound in 5 days? dA -512 1
In Problem find the family of all antiderivatives of each derivative. In(t – 5) t - 5 dm dt
Use differentiation to justify the formula e* dx = e + C
An environmental protection agency estimates that the rate of seepage of toxic chemicals from a waste dump (in gallons per year) is given bywhere t is the time in years since the discovery of the
The marginal price for a weekly demand of x bottles of shampoo in a drugstore is given byFind the price–demand equation if the weekly demand is 150 when the price of a bottle of shampoo is $8. What
Find the amount A in an account after t years if dA 0.02A and A (0) 1,000 dt
A psychologist found that, on average, the rate of learning a list of special symbols in a code N′(x) after x days of practice was given approximately by the following table values:Use left and
Find the amount A in an account after t years if dA 0.01A and A (0) = 5,250 dt
In Problem does the given differential equation model unlimited growth, exponential decay, limited growth, or logistic growth?y' = 10,000 - y (А) (В)
Find the equation of the curve that passes through (2, 10) if its slope is given byfor each x. dy 6. бх + 1 dx
In Problem find each indefinite integral. (Check by differentiation.) | (5e + 4) dz
In Problem calculate the definite integral, given that .4 .5 61 x dx = 7.5 x dx = 21 x² dx 3 4
In Problem calculate the definite integral, given that .4 .5 61 x dx = 7.5 x dx = 21 x² dx 3 4
Find each integral in Problem (In x)2
Find each integral in Problem x(x³ - 1)2 dx
In Problem find each indefinite integral. (Check by differentiation.) 3x2 dr x-
In Problem(A) Find the average value of each function over the indicated interval.(B) Use a graphing calculator to graph the function and its average value over the indicated interval in the same
(A) Find the average value of f(x) = 3√x over the interval [1, 9].(B) Graph f(x) = 3√x and its average over the interval [1, 9] in the same coordinate system.
Find each integral in Problem TV6 - x xp: V6- x
In Problem discuss the validity of each statement. If the statement is always true, explain why. If it is not always true, give a counterexample. If S"f(x) dx = 0, then f(x) = 0 for all x in [a,
In Problem(A) Find the average value of each function over the indicated interval.(B) Use a graphing calculator to graph the function and its average value over the indicated interval in the same
Find each integral in Problem xV16 — х dx
In Problem discuss the validity of each statement. If the statement is always true, explain why. If it is not always true, give a counterexample. If f(x) O for all x in [a, b], then f(x) dx = 0.
In Problem find the particular antiderivative of each derivative that satisfies the given condition.C′(x) = 9x2 - 20x; C (10) = 2,500
Find each integral in Problem (х + 1)%dr °dx
In Problem(A) Find the average value of each function over the indicated interval.(B) Use a graphing calculator to graph the function and its average value over the indicated interval in the same
In Problem find the particular antiderivative of each derivative that satisfies the given condition. dx 10 x(1) = 25 dt Vi
Find a function y = f(x) that satisfies both conditions: dy 9x?e" dx f(0) = 2
In Problem find the particular antiderivative of each derivative that satisfies the given condition.R′(x) = 500 - 0.4x; R (0) = 0
Evaluate the integrals in Problem xV2r2 - 3 dx 2
In Problem find the particular antiderivative of each derivative that satisfies the given condition. dR 50 R(1) = 50 dt
In Problem discuss the validity of each statement. If the statement is always true, explain why. If it is not always true, give a counterexample.If f(x) = 2x on [0, 10], then there is a positive
Evaluate the integrals in Problem x - х — 1 -dx Jox?- 2х + 3
In Problem find each indefinite integral and check the result by differentiating. x(x² + 3)
In Problem discuss the validity of each statement. If the statement is always true, explain why. If it is not always true, give a counterexample.If f(x) = 2x on [0, 10] and n is a positive integer,
In Problem find each indefinite integral and check the result by differentiating. x(x² + 5) dx
In Problem find the particular antiderivative of each derivative that satisfies the given condition. dy 6e' – 7; y(0) = 0 dt
In Problem find the particular antiderivative of each derivative that satisfies the given condition.f′(x) = 4x-2 - 3x-1 + 2; f(1) = 5
In Problem discuss the validity of each statement. If the statement is always true, explain why. If it is not always true, give a counterexample.If the area under the graph of f on [a, b] is equal to
Problem refer to the following figure showing two parcels of land along a river:You want to purchase both parcels of land shown in the figure and make a quick check on their combined area. There is
In Problem find the particular antiderivative of each derivative that satisfies the given condition.f′(x) = x-1 - 2x-2 + 1; f(1) = 5
Evaluate the integrals in Problem e* - er xp- (e*+ e*)2
In Problem discuss the validity of each statement. If the statement is always true, explain why. If it is not always true, give a counterexample.If f is a decreasing function on [a, b], then the area
In Problem find each indefinite integral and check the result by differentiating. x - 5 dx
In Problem find the particular antiderivative of each derivative that satisfies the given condition. dy = 3 - 2e'; y(0) = 2 %3D dt
In Problem find each indefinite integral and check the result by differentiating. 2V - 3 dx
Problem refer to the following figure:Use L6 and R6 to approximate ∫52 (0.25x2 - 4) dx. Compute error bounds for each. (Round answers to two decimal places.) Describe in geometric terms what the
Use a numerical integration routine to evaluate each definite integral in Problem (to three decimal places). ~3.5 x In x dx 1.7
Use a numerical integration routine to evaluate each definite integral in Problem (to three decimal places). 0.6 1 -0.5 V1 - x?
In Problem find each indefinite integral and check the result by differentiating. |r*(3x – 5) dx
Problem refer to the following figure:Use L5 and R5 to approximate ∫61 (0.25x2 - 4) dx. Compute error bounds for each. (Round answers to two decimal places.) Describe in geometric terms what the
Use a numerical integration routine to evaluate each definite integral in Problem (to three decimal places). -3 xe dx -2
In Problem find each indefinite integral and check the result by differentiating. x2(4x + 7) dx
In Problem find each indefinite integral. 2x4 dx .3
Use a numerical integration routine to evaluate each definite integral in Problem(to three decimal places). 1 dx -21 + x²
For Problem use derivatives to determine whether f is increasing or decreasing on the given interval. Use L4 or R4, whichever is appropriate, to give an overestimate of the signed area on the given
In Problem use a graphing calculator to graph the given examples of the various cases in Table 1.Unlimited growth:y = 1,000e0.08t0 ≤ t ≤ 150 ≤ y ≤ 3,500 Table 1 Exponential
Use a numerical integration routine to evaluate each definite integral in Problem (to three decimal places). 2.5 In x .2 0.5
In Problem the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your
Find a function y = f(x) that satisfies both conditions: dy 3x - x2 dx f(1) = 5
In Problem does the given differential equation model unlimited growth, exponential decay, limited growth, or logistic growth?y' = 0.43y (А) (В)
In Problem calculate the definite integral, given that .4 .5 61 x dx = 7.5 x dx = 21 x² dx 3 4
In Problem find each indefinite integral. (Check by differentiation.) 4 + u du
In Problem(A) Find the average value of each function over the indicated interval.(B) Use a graphing calculator to graph the function and its average value over the indicated interval in the same
Find each integral in Problem er (e + dr 2)2
In Problem does the given differential equation model unlimited growth, exponential decay, limited growth, or logistic growth?y' = -0.0152y (А) (В)
In Problem the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your
Find each integral in Problem e dx e* + 3
In Problem does the given differential equation model unlimited growth, exponential decay, limited growth, or logistic growth?y' = 2.5y(300 - y) (А) (В)
Evaluate the integrals in Problem ON
In Problem calculate the definite integral, given that .4 .5 61 x dx = 7.5 x dx = 21 x² dx 3 4
In Problem find each indefinite integral. (Check by differentiation.) dx 4x3
Find each integral in Problem r'(2r* + 5)° dx
In Problem find the general or particular solution, as indicated, for each differential equation. dx 4x dt
In Problem the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your
Find each integral in Problem (1 + x²)² 0.
Evaluate the integrals in Problem xe dx хе
In Problem calculate the definite integral, given that .4 .5 61 x dx = 7.5 x dx = 21 x² dx 3 4
In Problem find the general or particular solution, as indicated, for each differential equation. dx -5t dt
In Problem find each indefinite integral. (Check by differentiation.) du Vu
Find each integral in Problem •3 dx .2 +x
In Problem find the general or particular solution, as indicated, for each differential equation. dx = 4t dt
Find each integral in Problem 1 dx -3 V2 - x
In Problem find each indefinite integral and check the result by differentiating. 1 + x dx 4 + 2r + x
In Problem find the general or particular solution, as indicated, for each differential equation. dx -5x dt

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