Consider the region bounded by the curve y = 4x2 - x3 , the x-axis, and the lines x = 1 and x = 3. The region is rotated about the y-axis. Use shell method to find the volume of the solid of revolution. Express your answer in exact form.

Q: Find aw/as and aw/at using the appropriate Chain Rule. Function Values w = y³ - 5x²y x = es, y = et…

A: Given query is to find indicated partial derivatives.

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A: need to find out the critical point point of absolute maximum, absolute minimum.

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A: Given:        fx,y=arctanyx , 2,-2     fxx,y=∂∂xarctanyx                   =1yx2+1∂∂xyx taking y as…

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Q: Find the volume of the parallep lapiped with adjacents edges PQ, QPR, PS where PLO, -4,₁-4), Q (²-1,…

A: Concept: The volume of a parallelepiped with adjacent sides PQ, PR and PS is given by,…

Q: K Find the linearization L(x,y,z) of the function f(x,y,z)=√2+²+2 at the points (2,0,0), (5,6,0),…

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Q: Let f(x) = 4 sec (3x) f'(x) =

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Q: Solve for x in the triangle. Round your answer to the nearest tenth. 40°

A: For angle 40° Base= 6 and hypotenuse= x

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

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Q: Which of the following shows the simplified function of cscxsin 01 -1 tan x O cotx

A: Topic - Trigonometry We are given, csc x sinπ2-xWe know that,sinπ2-x=cos(x)

Q: radius of a sphere increases at a rate of 7 centimeters per second. Find the radius of the sphere…

A: Given query is to find the radius of the sphere.

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Q: |s sin³ 50 √ cos 50 de

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Q: esigning a Norman Window  A Norman window has the shape of a rectangle surmounted by a semicircle.…

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Q: Write the equation of the line in slope-interecept form that passes through (4,6) and (4,-3). Then…

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Q: 1. A chord passing through the focus of x²= 8y has one end at the point (-8,8). What is the other…

A: As per our guideline we can solve maximum one question you can repost other question

Q: Suppose that the length 7, width w, and area A = lw of a rectangle are differentiable functions of…

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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: 3 [(1 + 5a)'di

A: Solve the integral

Q: g(x) = 2 x²_4 3x²+x-4

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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: Chapter 6 11) Find the product (3 + 3x) (-4 + 3x)

A: Topic = Algebra As per guidelines , At a time only one question can be answered. Please repost for…

Q: O-11 60

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Q: Solve the right triangle. Round your answers to the nearest tenth. 49° a 17 m b = a = b = 0 X

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Q: Given f (x) O-3 O 0 0 1 x+2 =2+2,g(x) = *=², find (ƒ + g) (1)? =

A: See the answer below

Q: Suppose that the length 7, width w, and perimeter P of a rectangle are differentiable functions of…

A: Topic = Derivative

Q: Find the indefinite integral. (Use C for the constant of integration 2 cosh(√x) X dx

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Q: Find the indicated partial derivatives of f(x, y) = 9x³y² using the limit definition. The limits…

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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…

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Q: If f(x) = sin(x¹), find f'(x) Find f'(2) (round to 3 decimal places)

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Q: The radius of a circle increases at a rate of 2 m/s. Find the rate at which the area of the circle…

A: Given: the radius of a circle increases at a rate of 2m/s. We need to findthe rate at which the area…

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Q: Consider the region bounded by the curve y = 27x − x 4 and the x-axis. Use the trapezoidal rule with…

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Q: When the cost of producing a VCRS is given by C(x) the average cost for each VCR is C(x) x =…

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Q: The graph of y = g(x), shown below, consists of straight lines and a semicircle. Using known area…

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Q: K Suppose that T is to be found from the formula T=x (eY+ ey), where x and y are found to be 5 and…

A: Concept: Formulas used (f·g)'=f'g+fg'eln(a)=addxex=ex

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

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Q: To calculate the integral 3 /VR²³116 dr dx x² + 16 we want to make the trigonometric substitution

A: To solve the given integral.

Q: The area under the curve y Square Units 5x bounded by the lines x = 9 and x = 26 above the x axis is

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Q: What is one solution to the trigonometric equation 3cosx - sinx + 3 = 0 in the interval [0, 2m]? 0 O…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = surface y =…

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Q: Evaluate the given integral by changing to polar coordinates. JJ 5(x + y) dA where R is the region…

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Q: Determine the area of the region bounded by two the curves f(x) = x² – 18x + 28 and g(x) = 9x + 14.

A: Given: fx=x2-18x+28 and gx=9x+4 Graph between both the curves will be as following   Area between…

Q: 7x sin²(x) dx =___________ (Apply integration by parts method) O 7x tan(r) 7x cot (x) 7x In(sin(x))…

A: Topic = Integration

Q: Find the following using the table below. 1 2 3 4 12 x f(x) 3 4 f'(x) 2 3 1 g(x) 2 1 3 g'(x) 2 3 1…

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Q: Suppose z = x² sin y, x = −5s² + 3t², y = -6st. A. Use the chain rule to find 53 33 and as functions…

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Q: Use partial fractions to find the indefinite integral. (Remember to use absolute values where…

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