Consider the region bounded by the curve y = 27x − x4 and the x-axis.  Find the exact area of the region.

Q: 2 x² dx √4-x² 2

A: Let's solve given integration.

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Q: Find the absolute maximum and absolute minimum of the function f(x) = Provide your answer below:…

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Q: Find the limit. 5) lim 3x²+7x-2 x- 3x² - 4x-2

A: We will find the required limit.

Q: Let y = x5 ln x y' = = y" =

A: Topic - first and second derivative of a function We are given,  y=x5ln(x)we know…

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A: Given query is to find the time where velocity is 25.

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Q: If f(x) = √√7 - 4x, find a formula for f-¹(x).

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Q: A function and its graph are given. Find the domain. f(x)=-1-√√9-x² 54

A: Ye

Q: Find x. Round your answer to the nearest tenth of a degree. x = 山。

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Q: Set up, but do not evaluate, an Integral for the length of the curve. osys 21/12 O O x = 8 sin(y),…

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Q: Determine the area of the region bounded by two the curves f(x) = x² - 18x +36 and g(x) = 9x + 18.

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Q: In each of Exercises 1-14, D(x) is the price, in dollars per unit, that consumers are willing to pay…

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Q: (A) Eliminate the arbitrary constants. 1. xsiny + x²y = c 2. ax² + x + y² = 0 3. y = cx + c² + 1

A: Derivate the given equations to remove the constants.

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Q: Find the inverse for each of the following functions. f(x) = 9x + 1 f-¹(x) = g(x) = 12x³ - 5 g-¹(x)…

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Q: Find the values of the following limit. If a limit does not exist, type DNE in the entry box. limx→9…

A: Given; Limx-9(x-9)/[sqrt(x)-3].

Q: Determine the x-intercepts of the function g(x) = 2sin(2x) + 1 on the interval [0, 2m]. {끙끙} 17 117…

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Q: Let r(t) (4t+2, -4e¹, 2e #¹). Find the line (L) tangent to r(t) at t = 3. L: (x, y, z) = = +t

A: Given vector:- r→t=4t+2,-4et,2e-4t

Q: Check that the point (1, 1, 1) lies on the given surface. Then, viewing the surface as a level…

A: Given surface: x2-y2+4z2=4 and the point 1,1,1.

Q: pose f'(x) = √(x+3) and f(1) = 0. Find a formula for f(x) and show all of your work.

A: Given query is to find the function.

Q: Below are data on the population of a species of moths that inhabit an island and breed annually…

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Q: Find the partial derivatives of the function dw Or dw dw Ot W= √√2r² +58² +4t²

A: We can find the partial derivative of the function .

Q: Which of the following is the simplified expression of 1- 1 sece sin²e cos²0 O tan²e O sec²9 cose?

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Q: 5x² lim (x,y) (0,0) 2x² + 2y²

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Q: A particle moves along the x-axis so that its position at time 0 < t < 18 is given by x(t), whose…

A: We need to find out the intervals by the help of graph at which the function is function is…

Q: 1) Find the domain of the function f(x) = √3-x x+4

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Q: Solve for x in the triangle. Round your answer to the nearest tenth. 12 56°

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Q: Using a u-substitution, find (2+1) cos(2² + 2x) dr. Show all of your work, including what you choose…

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Q: Find the tangent, unit tangent, and unit normal vectors for the curve r(t) = (2t²+1, 2 sin(t),…

A: Given that, r(t)=&lt;2t2+1,2sin(t),ln(cos(t))&gt;We need to find tangent, unit tangent and unit…

Q: A particle moves along the x-axis so that at time t 0 its position is given by x(t) = t³ - 3t² 1.…

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Q: dx dt Please give an exact answer. If z³ = x³ + y², = dy -2, = dt dz dt Provide your answer below:…

A: To find derivative.

Q: limx→3 0 4 01 O O 3-x 4-√√²+7 O None of the above

A: We need to find: limx→3 3-x4-x2+7

Q: Find the particular solution of the differential equation x²y" + 11xy' +29y=0 (x > 0) satisfying the…

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Q: Evaluate the limit, using L'Hôpital's Rule if necessary. (If you need to use ∞ or -00, enter…

A: We need to evaluate the following limit using L'Hopital's Rule limx→∞ex39-x4 L'Hopital's Rule: If…

Q: Evaluate the definite integral. 7 1 √₁² 36 + (x + 5)² dx

A: Here, we have given a definite integral and be have to find its value so we will find it by using…

Q: Find the derivative of the function. 14 logg(t) t g' (t) = g(t) =

A: Topic = Derivative

Q: A tank contains 80 kg of salt and 1000 L of water. A solution of a concentration 0.04 kg of salt per…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of salt at time t…

Q: Determine whether the improper integral diverges or converges. 1 e2x + e-2x 1. converges O diverges…

A: Here we have to determine whether the improper integral diverges or converges. I=∫0∞1e2x+e-2xdx

Q: f(x) = sin² x, find f'(x) Find f'(4) (round to 3 decimal places)

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Q: Find the exact length of the curve. = (1 + x²) ³/2, 18 3 20 3 10 3 y 0≤x≤2

A: To find length of the curve.

Q: Find the area of the region that is bounded by the given curve and lies in the spect r-eº, 37 ≤0≤ 31…

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Q: Find the second derivative of the vector-valued function r(t) = (7t + 5 sin(t))i + (4t + 5 cos(t))j…

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Q: Find the following using the table below. 1 2 3 4 1 3 2 4 4 2 f(x) f'(x) 13 g(x) 23 14 g'(x) 1 2 4 3…

A: Explanation of the answer is as follows

Q: Find the transform of the given function by use of a table. f(t) = 5e-St_2e-2t A There is no correct…

A: By the options given it is the Laplace transform that you are asking. But next time please do…

Q: 3 +1 -dz [ + Z

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Q: ey = 25e4x-z+w 10z - w + 3x = -23 8y + 3w - x -z = 5 x+y-z + 4w = -10

A: The objective is to rearrange the  equations so that their associated matrix is ​​diagonally…

Q: The quantity demanded per month of an item is related to the unit price by the 45 demand equation…

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Q: Find the linearization L(x,y,z) of the function f(x,y,z) at the given points. f(x,y,z)= ex+cos (y+z)…

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