Q: For F(x) = x2 , F′(x) = 2x, making F(x) = x2 an antiderivative of ƒ(x) = 2x.
A: Given that Fx=x2. Compute the derivative. F'x=x2'=2x
Q: Find the most general antiderivative of f(x) = 2 – 2x³ + 7x° + 5x". Note: Any arbitrary constants…
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Q: Find the general antiderivative of f(x) = 3x + 15x-2 and check the answer by differentiating.…
A: ∫ xndx = ((x n+1)/(n+1))+C Power Rule: (d/dx) (xn ) = nxn-1
Q: Find the general antiderivative of f(x) = + C - 5x¹ x² +6√x
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Q: Evaluate the given function using homogeneous x- yArctan () dx + xArctan () dy = 0 A. 2yArctan ()…
A: We need to find solution of differential equation using homogenous.
Q: What is the antiderivative of f'(x) = 14x + 4 f(x) = What particular solution satisfies f( – 3) =…
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Q: compute for antiderivatives f(x)= x2-2 f(x) = x(x-4) f(x) = 3x2+2x+1
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Q: Find the general antiderivative of f(x) = 23x + 14x-2 and check the answer by differentiating.…
A: Given:- f(x) = 23x+14x-2 To find:- Anti derivative of f(x)
Q: Consider the function f(x) = 16x³ - 21x2 + 6x – 8. Find F(x) an antiderivative of f(x). F(x) =]
A: Topic - integration
Q: If F(x)=sinx+6x2−4 is an antiderivative of f(x) then f(x)=
A: If F(x) is antiderivative of f(x) , then f(x) is derivative of F(x) .
Q: a. Find the antiderivative of f(x) = -25x e F(x) = %3D
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Q: Consider the function f(x) = 5a°+ 5x® – 10x4 – 6. Enter an antiderivative of f(x)
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Q: Consider the function f(x) = 2x + 6x510x² - 4. = Enter an antiderivative of f(x). Do not enter +c as…
A: Here we have to find the integration.
Q: Let f(x) = 4x - 8x. Find F(x), the antiderivative function, if F(1) = 3.
A: Let f(x)=4x2-8xTo find the antiderivative function F(x)if F(1)=3
Q: Find an antiderivative F(x) with F'(x)=f(x)=7+18x2+14x6 and F(1)=0.
A: Find an antiderivative F(x) with F'(x)=f(x)=7+18x2+14x6 and F(1)=0.
Q: Find the antiderivative F(x) of f(x)= 3√x that satisfies F(1)=2
A: The given function, f(x)=x3
Q: Find the most general antiderivative of the functions: 1)f(X)= 2secxtanx-3sinx 2)f(X)=…
A: (1) Given, f(x) = 2secxtanx-3sinx ∫f(x)dx = ∫(2secxtanx-3sinx )dx = ∫(2secxtanx)dx -…
Q: 3 Consider the function f(x) = 5x° – 9x? + 2x – 6. An antiderivative of f(x) is F(x) = Ax* + Bæ® +…
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Q: Consider the function f(x)=5x^3−4x^2+7x−2An antiderivative of f(x) is F(x)=Ax^4+Bx^3+Cx^2+Dxwhere A…
A: Given function is
Q: The antiderivative of the function f(x) 4 + 11x is + 5.5z2 + c 4 5.5x + c -4 + 22.0x2 + c -4 +5.5x2…
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Q: Find an antiderivative F(x) with F′(x)=f(x)=11+24x^3+21x^6 and F(1)=0. Include a "+C" if…
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Q: Find the antiderivative of f(x)=e^(-1/x)/x^2
A: The answer of the above question is given below.
Q: Find f(x), the most general antiderivative of the function: f' (x) = 3x –
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Q: 3 If F(x) = 2x² x² is an antiderivative of f(x), find Provide your answer below: S-2f(x) dx = 1-2…
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Q: Find the general antiderivative of f(x) = 4x 4 - 6 T + C
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Q: Find constants c1 and c2 such that: G(x) = c1xe^−x + c2e^−x is an antiderivative of g(x) = 3xe^−x.…
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Q: I. Determine the general antiderivatives of the following functions: Show your solution . 7.…
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Q: Let f(x)=6x2+1f(x)=6x2+1.Enter an antiderivative of f(x) . . .
A: The given function is,
Q: Find the most general antiderivative of f(x) 2x-1+x.
A: Given, f(x) = 2x2 - 1 + x-2
Q: a.) If f(x) dx = 4x9 − 8x6 + C, find f(x). f(x) =
A: Given: ∫fxdx=4x9-8x6+c ..1 for finding fx, we differentiate…
Q: + 11x is The antiderivative of the function f(x) = 4 + 5.5x² + c 11 + 2.0z² + c + 5.5z² + c -4 +…
A: Anti derivative is obtained by integrating f(x)
Q: 2. Find the most general antiderivative of f(x) = 3+22 %3D
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Q: Consider the function f(x) = 5x³ 8x2 + 5x – 3. An antiderivative of f(x) is F(x) = Ax* + Bæ³ + Cx² +…
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Q: 4 + 9x is x2 The antiderivative of the function f(x) %3D
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Q: Consider the function f(x) = 2æ³ – 6x² + 8x – 9. An antiderivative of f(x) is F(x)= Aæ4 – Bæ³ + Cx²…
A: The given function is : f(x)=2x3-6x2+8x-9 The antiderivative of fx is the value of integral…
Q: Consider the function f(x) = 36x3 - 12x2 + 10x – 3. Find F(x) an antiderivative of f(x). F(2) =O
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Q: The antiderivative of the function f(x) +10z is -5 - 5.0z2+c -10 +2.5z2 + c +5.0z2 +c -5 + 5.0r +c…
A: To find:∫5x2+10x dx
Q: Consider the function f(x)=2x8+10x7−4x4−6 Enter the antiderivative of f(x)
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Q: Consider the function f(x) = 7x° + 9x° – 9 - 9. Enter the antiderivative of f(x) + C
A: T
Q: Consider the function f(x) = 6x' + 8x5 – 10x³ – 6. %3D - Enter the general antiderivative of f(x)
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Q: Consider the function f(x) = 2x° + 4x" – 8x² – 8. An antiderivative of f(x) is F(x) = Ax" + Bx™ +…
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Q: The antiderivative of the function f(x) = .9 + 9x³ is. 9. %3D -2 2.2x4 + c -2 + 2.2x4 -2 + 2.2x + c…
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Q: Find the general antiderivative, F(x), of the function f(x) = 2x -6x² +x+ 2.
A: we will answer the first question since exact one was not specified. Please resubmit the question…
Q: Show that F(x) = (x + 1)*(x – 2)3 is an antiderivative of the function f(x) = (7x – 5)(x + 1)³(x –…
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Q: Consider the function f(x) = 8x - 8x2 + 4x – 3. An antiderivative of f(x) is F(x) = Ax* + Bx + Cx² +…
A: We have to find antiderivative of f(x) or integral of f(x).
Q: Consider the function f(x)=9x^3−4x^2+8x−1. An antiderivative of f(x) is F(x)=Ax^4+Bx^3+Cx^2+Dx. What…
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Q: Find an antiderivative of the function f(x)=e2x.
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Q: 3 The antiderivative of the function f(x) = + 9x is x2 -3 4.5x2 + c 3 + 18.0a? + c 6- + 1.5x + c 3 +…
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Q: f(x) = Vx2 + xVx %3D
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Q: b) Let X₁, X₂, Xn-f(x) = {0x-(0*) x>1 e. w. find Suff. Comp. St.
A: Given that
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- The rate of change of an autocatalytic chemical reaction is kQxkx2 where Q is the amount of the original substance, x is the amount of substance formed, and k is a constant of proportionality. Factor the expression.f(x)= 36x + 3x^2 - 2x^3 where is f increasing? Where is f decreasing? For what x values, if any, does f a relative maximum and what x values, if any, does f have a relative minimum?Electrical generation from wind turbines (large "windmills") is increasingly popular in Europe and the United States. The fraction of the wind's energy that can be extracted by a certain type of turbine is f(x) = 1/2x(1 − x)2, where x is the fraction by which the wind is slowed in passing through the turbine. Find the fraction x that maximizes the energy extracted. x=
- The profit function of Acrosonic company is given by P(x)=-0.02x^2+300x-200,000 dollars, where x is the number of Acrosonic model F loudspeaker systems produced. Find where the function P is increasing and decreasing. 1.) Increasing a.) The profit function P is increasing on(7500,∞) b.) The profit function P is increasing on(7500,0) c.) The profit function P is increasing on (0,7500) d.) The profit function P is increasing on(∞,7500) 2.) Decreasing a.) The profit function P is decreasing on(7500,∞) b.) The profit function P is decreasing on(7500,0) c.) The profit function P is deccreasing on (0,7500) d.) The profit function P is decreasing on(∞,7500)Maximize P=3x1+5x2+2x3 Subject to: 3x1+4x2+5x3≤10 x1+3x2+10x3≤5 x1−2x2≤1 x1,x2,x3≥0 and give the value of x1 that maximizes P.For a certain company, the cost function for producing x items is C(x)=40x+200 and the revenue function for selling x items is R(x)=−0.5(x−110)2+6,050. The maximum capacity of the company is 140 items. 1.Assuming that the company sells all that it produces, what is the profit function? P(x)= . Hint: Profit = Revenue - Cost 2.What is the domain of P(x)? Hint: Does calculating P(x) make sense when x=−10 or x=1,000? 3.The company can choose to produce either 70 or 80 items. What is their profit for each case, and which level of production should they choose? Profit when producing 70 items = Profit when producing 80 items = 4.Can you explain, from our model, why the company makes less profit when producing 10 more units?
- For the function f (x) = x4 + 4x3 - 7x2 – 34x- 24 determin a) The intervals of increasing and decreasing b) The location of any maximum and minimum point c) The interval of increasing and decreasing d) The location of any point of inflation.Electrical generation from wind turbines (large "windmills") is increasingly popular in Europe and the United States. The fraction of the wind's energy that can be extracted by a certain type of turbine is f(x) = 1 2 x(2 − x)2, where x is the fraction by which the wind is slowed in passing through the turbine. Find the fraction x that maximizes the energy extracted.f=2x3−x2 Find all critical numbers that satisfy f′(c)=(f(b)−f(a))/b−a.
- tent line for h(x)=(2x^(2)+8x-5)^(2) at the x-value x=-1.Maximize f = 2x + 4y subject to x + y ≤ 9 2x + y ≤ 14 y ≤ 6. (x, y) = f =Find the intercepts of the function. f(x) = x2 − 6x Give the vertex, axis of symmetry, and intercepts. (If an answer does not exist, enter DNE.) vertex (x, y) = axis of symmetry x-intercept (x, y) = (smaller x-value) x-intercept (x, y) = (larger x-value) y-intercept (x, y) =
