Consider ζn = exp(2π√−1/n) ∈ C for n ∈ N. (a) Find [Q(ζn) : Q] (b) FIND {Q(ζn) : Q} (c) FIND Aut(Q(ζn)/Q)

Q: 3.1 Let f(x) be a periodic function with period 27. Express f(x) in terms of the Fourier (o 0<x<T…

A: Given function is fx=0      0&lt;x&lt;πx     π&lt;x&lt;2π To find the Fourier series of the above…

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Q: Find the periodic function f(x) = sinx + tan-+ sin- X + 23 + sin 2n+1 + tan ... 2n

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Q: 1 - cos(3x) lim 3x х> 0 1 + Зх — е e

A: We , have                Given      lim 1-cos3x1+3x-e3x     x70We have to evaluate the…

Q: Consider the elements σ1 = (152)(34) and σ2 = (163)(45) in S6. Calculate an element τ ∈ S6, written…

A: Given the elements σ1 = (152)(34) and σ2 = (163)(45) in S6. Calculate an elementτ ∈ S6, written as a…

Q: (a) In(1– x) +xe? (b) 2х 2x 1-cos(x) (d) V1+x-1 Check and briefly explain how to avoid the loss of…

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Q: (Hölder's Inequality

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Q: (3) positive Verify that the fourth-order ode u - u" - u = -wu has a solution with w 3 sech( /20…

A: Given: u''''-u''-u3=-ωu  ⋯1 We have to verify this fourth-order ode. Also determine ω.

Q: 6. Setting æ = cos 0 show that T.(e) = [(- + ivI- =')" + (* - ivī- =')"] n where i = V=1.

A: This immediately follows as a consequence of De Moivres formula which states that e^(it)=cos t + i…

Q: Inn In(Inn) limn→02n=3

A: To find the given limit

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Q: f(t) = 8 + 6t+2t², for- n<t<π, Show Transcribed Text and extend to a 2π periodic function.

A: The given function is ft=8+6t+2t2  for -π&lt;t≤π. To extend the function to a 2π periodic function.…

Q: 15. If an+2 = 3an+1 - 2an and ao = 3, a1 = 4, then an = O 3(2") - 3" + 1 O 5(2") - 2(3") O 7(2") -…

A: See the attachment

Q: ) prove thaE cos ( x) dx =- T e x" + x2 +l 213

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Q: Let f(x, y, z) = x³e" Vz² + 5 and let x = rt², y = r2t², and z = sin(t) cos(r). (a) Draw a tree…

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Q: Show that if p is a prime number, a and b are positive integers and p | ab, then p | a or p | b.

A: The objective is to prove that if p is a prime number, a and b are positive integers and p | ab,…

Q: Solve (tan(z) - 1) (3 tan(x) +√3) o over the interval (-∞, ∞).

A: Here is the solution:

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A: Here given that for 2π periodic function, f(x)=cos2(x)+sin3(x). We calculate a0,a1,a2,an(for…

Q: identity

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Q: If g (x) = x* - 2x3 – 7x² + 8x + 16,find g (-1), g (-2),g (2),g (3)

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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A: Given: The product of f1x and f2x is an even function. f1x is an odd function. To determine: The…

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A: Given,           f(x) = x - (2x + 1)2 ;    x ≤ 1ln(x)ex        ;            x &gt; 1    and the…

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Q: The Gamma Function I (n) is defined by I (n) = xn-le-ªdx,n > 0. (а) Find Г (1), Г (2), and Г (3).…

A: We will show the given results.

Q: (c) L-¹ 2s 14 { (8+3)(8 + + +28+5) 4e-3s -1 s² (s+4)) (d) L-¹ {

A: As per the policy of bartleby the provisions is to solve only one question at a time  but here  I am…

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A: given function fx=sinxgx=-35sin2x+60°-3

Q: If x(t) , X(f), then show that x(t) cos (@- w. 2 (@ + w.).

A: To find fourier transfer of given system first expand cos wt in form of Eulers form then use the…