Use Shell Method to find the volume of the solids of revolution described in each item. Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = x² and the x - axis for the interval 1 < x < 2.

Q: Given the function f(x) = -x* - 4x determine its critical points and classify them, determine the…

A: We have to find the points and check the nature of function.

Q: 7. Let f(x) = -3x + 9x - 3. a. Determine the x values where f"(x) = 0. b. Fill in the table below to…

A: In this question we have to find first three subpart.

Q: dx (9 – 4.x²)³/2 2,3/2

A: Use substitutions to make it more simple

Q: Find an equation of the tangent line to the graph of x* + 3xy? + y = 15 at the point (1, 2).

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Q: Given the function f(x) = -xr* – 4x determine its critical points and classify them, determine the…

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Q: 2+Secx-

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Q: Determine the local maximum and minimum values and the saddle points of the function: f(x,y)…

A: Given, f(x,y) = y3 + 3x2y - 6x2 - 6y2 + 2

Q: Find the first three nonzero terms of the Maclaurin expansion of the function. f(x) = 8 cos TX ...…

A: The Maclaurin series is given by  f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: 18. Find [ 2x°(2x* -1) dx

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Q: Find the velocity and acceleration vectors in terms of u, and ug- de r= a(7- sin 0) and =7, where a…

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Q: Please answer the question; correctly, thank you

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Q: 2" an 2n + 1 (-1)"-1 An 5"

A: The given sequence,1. an=2n2n+12. an=-1n-15n

Q: 1. Determine the exact value(s) of k for which the planes x– 2y + kz + 7= 0 and x– 2y – 2 = 0 have…

A: Note: According to our answering guidelines we have to answer only one question if multiple…

Q: The area of the region that lies to the right of the y-axis and to the left of the parabola æ = 2y –…

A: topic- Area bounded by curves

Q: 5+ 4. 2 1+ -5 -4 /-3 -2\1 1 5 -1 -2 -3 -4 -5 + 3.

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Q: QV Optimize the function Z = xị + xị Subject to: x1 + x2 = 4 x1, x2, 20 Using Lagrange multipliers.

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Q: 8 Evaluate ( - 12vt)dt Select one: 666 a. 654 13 664 O C. 15 660 Od. 15

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Q: To find the distance across a small lake, a surveyor has taken the measurements shown. Find the…

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: Use derivative and unit tangent formula for finding it.

Q: 4. Find the Linearization of f (x) = sinx at a 5. Provide your answer as L(x) =? %3D

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Q: 27. Find the magnitude of the resulting force. Round to the nearest Newton. B: 11.1 N, 111° A: 10.0…

A: Solution: Given

Q: b). Using gamma function, evaluate Sx6 e-2x dx

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Q: Let -1 <a < 1, the series r na" is the power series representation of the n-1 function Select one:…

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Q: [9]. Suppose that a ball is dropped from an initial height of 300 feet, and subsequently bounces…

A: The initial fall h=300 The first rise &amp; fall 2*.9× 300 The 2nd rise &amp; fall…

Q: 3. Determine the balance A for $7,000 invested at a rate of 4.5% for 20 years, compounded a. Monthly…

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Q: v(x² – y + x)dx + (x² – 2y) dy = 0 %3D

A: Topic:- solution of differential equation

Q: Refer to the figure below to find the limit lim f(x). X - 00 3.5- 2.5- 1.5- 1- 0.5- 2.

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Q: Determine the antiderivatives of the following functions: 1. V36-x² dx 2. J 9x2+36dx 1 S- x In…

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Q: Qu 1 a). Determine the LaPlace transform of the differential equation y"- y = e2 ; y(0) =0 and y"(0)…

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Q: n Apply the Integral Test to the series E n=1 n²+1

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Q: dy given the dx Use implicit differentiation to determine equation x° + y? 10. - dy dx

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Q: position in feett seconds after it starts moving is given by s(t)=D9t/t erage rate of change in…

A: Topic:- application of derivatives

Q: Find the area of the region between the curves y = æ and y = Va. Area between curves

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Q: 5. The cost C (in dollars) of producing x units of a product is given by the following. C= 3Vx + 400…

A: Use derivative for finding the marginal cost .

Q: Find T, N, and k for the space curve, where t>0. r(t) = (5 cos t+ 5t sin t)i + (5 sin t- 5t cos t)j…

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Q: Related Rates A rock is thrown into a still pond. The circular ripples mové outward from the point…

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Q: Find the following limit. Answer in either integer or fraction form. NO DECIMAL APPROXIMATIONS. If…

A: To find the limit.

Q: dz dz and at 3. Let z = x? + y, a = 2st and y = s - t2. Compute for

A: Answer (3)  Let z = x2 + y3 , x = 2st and y = s - t2  We have to compute for ∂z/∂x and ∂z/∂t

Q: For the power series E (х-3)" find the interval of convergence. n=2 n5"

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Q: Determine whether each sequence having the given nth term is monotonic. a. a, = 3+ (-1)"

A: If {an} is an increasing sequence or {an} is a decreasing sequence we call it monotonic If a…

Q: Determine the first derivative for each of the following functions. Remember to "Tidy" up your final…

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Q: . Use Shell Method to find the volume of the solids of revolution described in each item. Find the…

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Q: fi(x)-2• sin(x) -3- R 3- 5- 3.* 4. 4 2 -2

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Q: 1. S-7e*dx 2. S(2ex – 6*)dx S(3)dx 3.

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Find the number(s) b such that the average value of f(x) = 6x - 42x + 70 on the interval 0, 6 is…

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Q: L Find the point/s of intersection of each of the following figures given below, draw the element…

A: topic - Area bounded by curves

Q: Sketch the region enclosed by 2y = 5/a, y = 4, and 2y + 2æ = 7. Decide whether to integrate with…

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Q: 1. When do find a volume by the slic (a) A type I region rotated abou (b) A type I region rotated…

A: Given question:- When do find a volume by the slicing method? Circle all that apply.

Q: f'(x) =-+e²* +x²and f(1)=. Find f(x) Given

A: Here, given that: f'(x)=1x+e2x+x3⇒f(x)=∫1x+e2x+x3dx+C⇒f(x)=∫1xdx+∫e2xdx+∫x3dx+C⇒f(x)=ln…

Q: the line tangent to the graph of f at the indicated value of x. Find the value(s) of X where the…

A: The given equation is  f(x)=ln(4-x2+2x4); x=1.