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college mathematics for business

Questions and Answers of College Mathematics For Business

Provident Bank offers a 10-year CD that earns 2.15% compounded continuously.(A) If $10,000 is invested in this CD, how much will it be worth in 10 years?(B) How long will it take for the account to
A streetlight is on top of a 20-foot pole. A person who is 5 feet tall walks away from the pole at the rate of 5 feet per second. At what rate is the tip of the person’s shadow moving away from the
In Problem find f′(x) and simplify. Зх + 5 x² – 3 f(x) %3D
In Problem find the logarithmic derivatives.f(p) = 100 - 3p
In Problem find f′(x) and simplify.f(x) = (x2 + 2) (x2 - 3)
In Problem find f′(x) and simplify.f(x) = ex2 + 3x + 1
In Problem find the logarithmic derivatives.A(t) = 400e0.049t
It can be shown that the number e satisfies the inequalityIllustrate this condition by graphingy1 = (1 + 1/n) ny2 = 2.718 281 828 ≈ ey3 = (1 + 1/n) n + 1in the same viewing window, for 1 ≤ n ≤
In Problem find f′(x) and simplify. x? + 1 f(x) %3D 2r 3
In Problem find f′ (x).f(x) = ln x2 + 4ex
In Problem find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent.f(x) = 225 + 65x; x = 5
In Problem find f′(x) and simplify.f(x) = 3e-6x
Find y′ for y = y(x) defined implicitly by ln y = x2 - y2, and evaluate at (1, 1).
In Problem find f′(x) and simplify.f(x) = 6e-2x
In Problem find y′ in two ways:(A) Differentiate the given equation implicitly and then solve for y′.(B) Solve the given equation for y and then differentiate directly.x3 + y3 = 1
In Problem replace ? with an expression that will make the indicated equation valid. d 유(4-27):-3(4-2x)2 2 2r) = 3(4 – 2r)²_? dx
If $6,000 is invested at 10% compounded continuously, graph the amount in the account as a function of time for a period of 8 years.
In Problem replace ? with an expression that will make the indicated equation valid. d (5-2x) = 6(5 – 2x) ? dx
In Problem use logarithmic properties to write in simpler form.ln xy
Use a calculator and a table of values to investigateDo you think this limit exists? If so, what do you think it is? lim 1 + S-0 S S
Use a calculator and a table of values to investigateDo you think this limit exists? If so, what do you think it is? 1/n lim (1 + n)
Find y′ for y = y(x) defined implicitly by x - y2 = ey, and evaluate at (1, 0).
In Problem find f′(x) and simplify.f(x) = (0.5x - 4) (0.2x + 1)
In Problem use a calculator to complete each table to five decimal places. [1 + (1/n)]" 10 2.593 74 100 1,000 10,000 100,000 1,000,000 10,000,000 e = 2.718 281 828 459...
In Problem find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places.f(x) = 4x2 - ln x; x = 5
In Problem find f′(x) and simplify.f(x) = e5x
Find x′ for x = x(t) defined implicitly by x3 - 2t2x + 8 = 0, and evaluate at (t, x) = (-2, 2).
In Problem use a calculator to complete each table to five decimal places. [1 + (1/n)]" 10 2.593 74 100 1,000 10,000 100,000 1,000,000 10,000,000 e = 2.718 281 828 459...
In Problem find f′(x) and simplify.f(x) = (0.4x + 2) (0.5x - 5)
Find y′ for y = y(x) defined implicitly by the equation x2 - 3xy + 4y2 = 23, and find the slope of the graph at (-1, 2).
In Problem find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places.f(x) = 4x2 - ln x; x = 2
In Problem find f′(x) and simplify.f(x) = (3x2 + 5)5
The radius of a spherical balloon is increasing at the rate of 3 centimeters per minute. How fast is the volume changing when the radius is 10 centimeters?
In Problem find f′(x) and simplify.f(x) = (x2 + 1) (2x - 3)
In Problem find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places.f(x) = 500 - 6x; x = 75
In Problem find f′ (x).f(x) = ex + x - ln x
In Problem find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places.f(x) = 420 - 5x; x = 55
In Problem find f′(x) and simplify.f(x) = (4 + 0.2x)5
A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is increasing by 2 feet per second, how fast is the area changing when the radius is 10 feet?
A boat is being pulled toward a dock as shown in the figure. If the rope is being pulled in at 3 feet per second, how fast is the distance between the dock and the boat decreasing when it is 30 feet
In Problem find f′ (x).f(x) = 9ex + 2x2
Find the indicated derivatives in Problemy′ for y = ln(2x3 - 3x)
In Problem find f′ (x).f(x) = x3 - 6ex
In Problem find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places.f(x) = 420 - 5x; x = 25
In Problem replace ? with an expression that will make the indicated equation valid. d 1 In (x - x') dx ? X - x3.
In Problem replace ? with an expression that will make the indicated equation valid. d 1 In(x* + 1) dx ? x* + 1 ||
In Problem find f′(x) and simplify.f(x) = (5 - 2x)4
In Problem find f′(x) and simplify. Зх — 4 3x f(x) 2х + 3
In Problem find f′(x) and simplify.f(x) = 3xex
In Problem find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places.f(x) = 580; x = 300
In Problem find f′(x) and simplify. 2x + 3 f(x) x - 2
In Problem replace ? with an expression that will make the indicated equation valid. etr-2 ? dx
Use a calculator and a table of values to investigateDo you think the limit exists? If so, what do you think it is? lim (1 +
In Problem find y′ in two ways:(A) Differentiate the given equation implicitly and then solve for y′.(B) Solve the given equation for y and then differentiate directly.x + ln y = 1
In Problem find f′(x) and simplify. 3x f(x) 2х + 1
In Problem find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places.f(x) = 45; x = 100
In Problem find y′ in two ways:(A) Differentiate the given equation implicitly and then solve for y′.(B) Solve the given equation for y and then differentiate directly.x2 - ln y = 0
In Problem find f′ (x).f(x) = -7ex - 2x + 5
In Problem replace ? with an expression that will make the indicated equation valid. d = er²+1 +1 ? dx
In Problem find f′(x) and simplify. f(x) %3D х — 3
In Problem find y′ in two ways:(A) Differentiate the given equation implicitly and then solve for y′.(B) Solve the given equation for y and then differentiate directly.4x2 - ey = 10
In Problem replace ? with an expression that will make the indicated equation valid. d (3x + 7)5 5(3x2 + 7) _? dx
In Problem use logarithmic properties to write in simpler form. In- v'w
In Problem find f′ (x).f(x) = 5ex + 3x + 1
In Problem find the relative rate of change of f(x).f(x) = 12 + 5 ln x
Find the slope of the line tangent to y = 100e-0.1x when x = 0.
In Problem use logarithmic properties to write in simpler form. uv In W
In Problem find y′ in two ways:(A) Differentiate the given equation implicitly and then solve for y′.(B) Solve the given equation for y and then differentiate directly.x + ey = 4
If $4,000 is invested at 8% compounded continuously, graph the amount in the account as a function of time for a period of 6 years.
In Problem use the price–demand equation 2p + 0.0lx = 50, 0 ≤ p ≤ 25.If p = $9 and the price is increased, will revenue increase or decrease?
In Problem find the relative rate of change of f(x).f(x) = 7 + 4e-x
In Problem use the price–demand equation 2p + 0.0lx = 50, 0 ≤ p ≤ 25.Find all values of p for which demand is elastic.
In Problem find f′(x) and simplify.f(x) = (x - 3) (2x - 1)
In Problem find y′ in two ways:(A) Differentiate the given equation implicitly and then solve for y′.(B) Solve the given equation for y and then differentiate directly.6x2 + y3 = 36
In Problem replace ? with an expression that will make the indicated equation valid. d (3x + 4)4 = 4(3x + 4)3 ? dx
In Problem use the price–demand equation 2p + 0.0lx = 50, 0 ≤ p ≤ 25.Find the elasticity of demand when p = $15. If the $15 price is increased by 5%, what is the approximate percentage change
In Problem find f′(x) and simplify.f(x) = 5x2 (x3 + 2)
In Problem find y′ in two ways:(A) Differentiate the given equation implicitly and then solve for y′.(B) Solve the given equation for y and then differentiate directly.2x + 9y = 12
In Problem use logarithmic properties to write in simpler form.ln x5
In Problem find the relative rate of change of f(x).f(x) = 35x - 0.4x2
In Problem use the price–demand equation 2p + 0.0lx = 50, 0 ≤ p ≤ 25.Find the elasticity of demand E(p).
In Problem find f′(x) and simplify.f(x) = 2x3 (x2 - 2)
In Problem find y′ in two ways:(A) Differentiate the given equation implicitly and then solve for y′.(B) Solve the given equation for y and then differentiate directly.-4x + 3y = 10
In Problem use logarithmic properties to write in simpler form. In y
In Problem use logarithmic properties to write in simpler form.ln ex
In Problem use the given equation, which expresses price p as a function of demand x, to find a function f(p) that expresses demand x as a function of price p. Give the domain of f(p).p = ln (500 -
In Problem find f′(x)f(x) = x ln 3 - 3 ln x
In Problem solve for the variable to two decimal places.4,840 = 3,750e4.25r
In Problem use the price–demand equation 2p + 0.0lx = 50, 0 ≤ p ≤ 25.Express the demand x as a function of the price p.
In Problem find (A) The derivative of T(x) /B(x) without using the quotient rule, and (B) T′(x) /B′(x). Note that the answer to part (B) is different from the answer to part
In Problem if it is possible to solve for y in terms of x, do so. If not, write “Impossible.”y2 + exy + x3 = 0
In Problem use the given equation, which expresses price p as a function of demand x, to find a function f(p) that expresses demand x as a function of price p. Give the domain of f(p).p = 80 - 10 ln
In Problem solve for the variable to two decimal places.956 = 900e1.5r
For y = 3x2 - 5, where x = x(t) and y = y(t), find dy/dt if dx/dt = 3 when x = 12.
In Problem find (A) The derivative of T(x) /B(x) without using the quotient rule, and (B) T′(x) /B′(x). Note that the answer to part (B) is different from the answer to part
In Problem if it is possible to solve for y in terms of x, do so. If not, write “Impossible.”5x + 3y = ey
In Problem solve for the variable without using a calculator.ln x = 2
In Problem use the given equation, which expresses price p as a function of demand x, to find a function f(p) that expresses demand x as a function of price p. Give the domain of f(p).p = 45 - e x/4,
In Problem find f′(x)f(x) = 12ex - 11xe
In Problem solve for the variable to two decimal places.10,000 = 7,500e0.085t

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