Given that S' = {e® : 0 € R}, where e" = cos(0) + i sin(0). %3D Show that S' is a group under multiplication ei0 eit2 = ei(01+O2).

Q: Suppose f(x) = sin 4-x). Evaluate: x) dx (A - 3cos FC B -cos 3 X-4+ C 3 Cos 3 (D) 3cos -x- 4)+C

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Q: if it was S={a+b/2 :a,bEZ} and (S,.) where(.) is a ordinary muliplication…

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Q: (x²+y² 4. If u = sin-1 ( ) then prove that by Euler's theorem, x+Vy. ди X + y: дх ди 3 tan u. 2

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Q: Using Laplace and Inverse Laplace Transformation, find the particular solution of the following: a)…

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Q: Sketch a graph of x = -3 + cos(t), y =1+ sin(t), 0 < t < 27 COS 5+ 4-

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A: In this question, the concept of the Jacobian of functions is applied. The Jacobian of Gr,t is…

Q: 3) Evaluate ex*+¹sin (√x) dx].

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Q: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: Read each of the two statements carefully. Choose A(if both statements are true), B(if the 1st…

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Q: - IF z = tan2 -1 y Show that x- ây

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Q: Differentiate: y = cos(5 e* ) e11 COS

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Q: Integrate using Trigonometric Transformation cos 5 (In z)da a csc® (In æ)

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Q: Explain Perron-Frobenius Theorem.

A: According to Perron-Frobenius Theorem, there is a single largest real eigenvalue for a real square…

Q: Given that Le"}= - s- a 1 and that e = cos ot +isin ot , deduce the Laplace transforms for cos ot…

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Q: Evaluate S" -2n 1 cos³ w sinsw dw 2 O - 1/2 O 1/2 O 1

A: Please find attachment for the details solution

Q: Obtain _t Z { (e cos2t) * alt-1s4

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Q: Q2) A Differentiate the following ( 1)y= [(5x) (4- 2x)]²

A: As per bartleby guidelines we only give first question answers.

Q: B. Let ulr,e) = r"sin(ne). Find 4 2n-2 +u -nr Ure or

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Q: +1- 2 cos 0 for Z E C., show z"+ = 2 cos(n@) that %3D

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Q: 3) [I - cos х х

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Q: In what form should the particular solu tion be sought for the equation y(4) + 2y"' + y'" + 2y' =…

A: We will solve it by undetermined coefficient method Let the particular integral with respect to x is…

Q: Suppo se fCA) = gl hux). If gce)-3, gʻl2): 4, hl0): 2, and h'(0)=6 find f'c0).

A: we have given function f(x) = g(h(x))g(2)=3g'(2)=4h(0)=2h'(0)=6

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…

Q: Calculate the Fourier transforms of the following functions (you do not need to use any complex…

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Q: Sketch a bifurcation diagram for the equation x'=a+x-x^3  Identify all birfurcations.

A: Bifurcation diagram is used to study dynamical system. Stable or fixed points are obtained and then…