Find the volume, in cubic units, generated by revolving about the x-axis the area bounded by the curve y²+x-2y-1. the x-axis and the line x-2

Q: 6. Find the radius of convergence and the interval of convergence for E-0¹ (x-2)".

A: 6. The given power series     ∑n=0∞12nx-2n

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A: Explanation of the answer is as follows

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Q: Please determine if the sequence converges or diverges. \left(\frac{n!+6}{n!-2}\right)

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A: I am attaching image so that you understand each and every step.

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Q: Use the chain rule to find dz/t. z = x² + y² + xy, x = sint, y = et

A: Here we will find dz/dt,

Q: Find the area between f(x)=x²-12 and the x-axis from x = 0 and x = 2. The area is square units. ...

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Q: 6. Find the area of the region bounded by x = y³ − 4y² + 3y and the x = y² − y. 77 (a) A= square…

A: The region is bounded by the curve x=y3-4y2+3y and x=y2-y

Q: : Find area of triangle whose vectors P1(4,2,0), P2(-1,1,1), P3(0,4,3)

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Q: Problem 1. Solve these integrals using substitution (a) x(x-2)³ dx, (b) text² di dt.

A: The given integrals:a∫xx-25dxb∫te3t2dtWe will solve them using substitution.

Q: Use the graph of f(x) to determine the following limits. The domain of f(x) is x E R. If the limit…

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Q: u - If ü = 43 - 2k and = 2 - 3 + 7k, find 3u - 27.

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Q: For the parametric equations r(t) = √t+1 y(t) = t+1 compute dz/dt and dy/dt. Is there any point on…

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Q: Find the general solution of the given second-order differential equation. 30y" 19y' 5y = 0 -…

A: See the details solution in below

Q: 0. The equation 7(x) = 40cos(x-10)] + 160 describes how an element in a fur cyclically, where x is…

A: topic:- function

Q: 11.Sketch the graph of the region D and evaluate the double integral y dA, D = {(x,y)| 0≤ x ≤ ¹,0 ≤…

A: The region D is bounded by the below curves:x=0 to x=1; y=0 to y=x3.

Q: Solve the following linear programming problem.   ​Maximize: z= 39x+10y subject​ to: 8x+6y ≤48…

A: Given that, Maximize: z= 39x+10y subject​ to: 8x+6y ≤48   13x+y ≤48…

Q: Find the coordinates of a point on the parabola y=−x² where the slope of the tangent is 5. x+3x+4

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Q: Prove the identity. cos(x - 1) - sin(x + 1) = = 0 Use the Addition and Subtraction Formulas, and…

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Q: Consider the following equations. 124 O Sketch the region bounded by the graphs of the equations. y…

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Q: a-limx. 1x-4 Tollowing b- limx-o (sin (sin x) c- limx→→z 5x²+x³ 10x +2x5,

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Q: Find the average value of: f(x) = 8 sin x + 3 cos x on the interval [0,1] 3 Average value =

A: Solved below.

Q: Given f(x) = cos(x) - 2x² + 3x - 1, then f"(0) is equal to- Ο -5 Ο Ο Ο Ο Ο Ο -3 Ο -1 None of them O

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Q: Evaluate √t (3t-t²) dt

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Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(e, 1) =

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Q: find the explicit solution of y' +xy = x√ y

A: This is a basic differential equation problem

Q: Q/. Find the limit of the function * lim 4-√x²³+7 3 X

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Q: Consider the following functions. f₁(x) = 8, f₂(x) = cos²(x), f(x) = sin²(x) g(x) = c₁f₁(x) +…

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Q: An air traffic controller spots two airplanes at the same altitude converging to a point as they fly…

A: There are two planes on the XY axis.We are at the origin.  Plane X: The first plane is due west of…

Q: [(x+1)e(x²+2x) dx

A: Given :∫x+1ex2+2xdx

Q: Determine the number of points of intersection for the planes: T₁: 3x-6y + 12z - 6 = 0 and 7₂: 2x -…

A: We want to find number of points of intersection of two planes.

Q: Find the indefinite integral of the following function:

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Q: SUBJECT: DIFFERENTIAL EQUATION TOPICS Growth/Decay  Newton's Law of Cooling/Heating Mixture Simple…

A: Given that, A tank has pure water flowing into it at 10 liters/min. The contents of the tank are…

Q: The solution of differential equation y' + (cot x) y = 3 sin x cos x, x = (0,π). is:

A: Using Integrating Factor formula:

Q: The figure shows a region in the complex plane. Write an algebraic description of the shaded region.…

A: Given :Center : Z0=4+i

Q: Find the unit tangent vector T(7) for the line tangent to the space curve r(t) = (12 cost, 12 sint,…

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Q: 8. Let R be the region bounded by y = √25-2² and y = 3. Find the volume of the solid generated when…

A: I have stated the used formula in the solution.

Q: 2. Integral A e3A dA

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Q: A 30 6 12 ♡ E C D F Find the area of Square ABCD

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Q: 15. integral sin 4x cos 4xdx

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Q: Let F(x) = [² costdt. Find F'(x).

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Q: +[ƒ Given that 5 ≤ f(x) ≤ 6 for -4 ≤ x ≤7, use property 8 of Section 5.2 of the Stewart Essential…

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Q: f(x)=2x-7 and g(x) = -18 Given (a) Find (fog)(x). (b) Find (gof)(x). (c) Is the operation of…

A: Given :fx=2x-7gx=1x

Q: The following differential equation (+1)² + ² = sin a dy dx x has an order of 0 0 O 3 O 1 02

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Q: b) F (1) √x 1 -Jetr 1 + 2 dt.Using the 2nd Fundamental Theorem of Calculus, find 2 Given that F(x) =…

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