Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. TL y = 8 sin(x), y = 8 cos(x), 0≤x≤ ; about y = -1 4

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Q: QUESTION 15

A: answer is in next step

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A: Please see the answer below.

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A: Given :  the graph of f '

Q: II. Find d Do not simplify your answers. 1. log,(√2x² + y) + tan(z* — x") = sin−¹(x² − 1) + ½

A: This question can be solved using the concept of differentiation of implicit function.

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A: f(x)=13x3-52x2+4xa) Differentiatef'(x)=13.3x2-52.2x+4f'(x)=x2-5x+4For critical points…

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A: answer is in next step

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Q: a. Find the volume of the solid obtained by rotating the region bounded by y = x³, y = 8, and x = 0…

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A: We need to find domain and value of r(t).

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Q: tri(t): [r₁(t) r₂(t)] = r₁(t) x + x r₂(t). dt dt ri(t) = cos(t)i + sin(t)j + 6tk, r₂(t) = 5i + tk d.…

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A: a) limx→0-f(x)=-∞b)  limx→0+f(x)=2c) limx→0f(x)=Does not existd) f(0)=2

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A: Explained below

Q: Find sec 2x -dx. tan 2x cot82x (4sec 22x-1) (A) 12 1 1 I B 12 tan 2x 16 tan 82x Ⓒ -co1²2x-co1³21+ C…

A: Here is the solution

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A: Topic:- function and integration

Q: Question 3 x²+x+1 Sa 2x²+2+x³+x -D Sa x+2' - dx = [Aƒ (x) — B ln(g(x)]å + D rb dx 2 and if A = B<0,…

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Q: Find the arc length of the parametric curve. L x = 4 cos(t), y = 4 sin(t), z = 3t; 0≤t≤ T

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Q: Question 3 This question is not about solving the stated problem, but about understanding it. A…

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Q: 55. f(x) = x² + cos ¹x on [-1, 1]

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Q: dx secx+1

A: Given ∫dxsecx+1We do half angle substitution:=∫1tan2(x2)+11-tan2(x2)+1dxSubstitute…

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Q: Use the formula k(t) k(t) = = ||r' (t) x r"(t)|| ||r' (t) ||³ = 10t. r(t) = e¹0ti + e-tj to find…

A: We have to find k(t)

Q: 3. Evaluate lim x →∞ ९+2 -( if necessary, using L'Hôpital's rule) 1-x³

A: In this question we have to find limit.

Q: Question 4 Solve the equation: 1²+t+19-0. Fully simplify all answers, including non-real solutions

A: The given equation is: t2+t+19=0