Use the PMI to prove that for i = √-1 EC and kEN (cose + isine) = cos k0+isin k0, k≥ 2.

Q: Find the ACF of the following PSD's. 157 + 12 o2 (16 + w?) (9 +o? (i) Sxx(@)

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Q: .2п 0 cos² t 2 COS 13 + 12 cost dt

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Q: Q(3): Show that: (a) Vx Vo(r) = 0, and (b) V-VX E(F) = 0.

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: c2π 0 cos 2t 17 - 8 cost dt

A: Cauchy residue theorem is used to find the integral of a closed curve. Cauchy residue theorem says…

Q: 4. Then we can write (x + jy)" as R"eme and go back to write the result

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Q: Verify that and use this equation to evaluate 2-1(2-4) (Aª dx 1

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Q: - 75ec 3x+tan 3x(sec 3x+tan 3x) cos 3x dx (7sec 3x+tan 3x)In 7 + C 7secax+tan ax + C 7 In 3 3 O c B…

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Q: • 2π 0 1 1 + cos² t dt

A: ∫02π11+cos2tdt

Q: 31. ₁*√ (1 + 1) dt St √√t t) 33. T/4 1 + cos²0 cos²0 ST7/4 ӨР 32. /sece tane de

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Q: c2π cos² t 13+ 12 cost dt

A: The Cauchy Residue theorem is a part of the complex analysis. By using the Cauchy Residue theorem we…

Q: Evaluate by Residue Theorem/Formula do where a = your registration number first digit, (a + bcos0)²…

A: It is clear that : cosθ=z-1zzdθ=dziz For the given integral ,…

Q: •2πT 2 cos³ t + 3 cos² t dt

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Q: Show that M8 Σrk k= pk cos(ak) = −1+ 1-2 2(r2-2r cos a+1)

A: Using summation of infinite series in geometric series Sum = first term /(1- common…

Q: Qil classify the following sequncey © {√√√n } Ⓒ [to)" -n²} Ⓒ {²}

A: Given the Sequence: n -1n.n2 n-1n We need to classify the given sequences.

Q: Use the residue theorem to evaluate: o dx 0 x3+1 2n/3

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Q: Write do wn the form of particular By=gle) for each of the following g (x) solutiun to

A: For the given differential equation 4y''-4y'-3y=g(x) We need to find the form of a particular…

Q: Solve the following Exact ODE

A: This is a problem of DE.

Q: 1. Evaluate the following commutators: a) [p, x5] b) [cos kx, p]

A: These are the questions from the operator theory.

Q: ( sin(3x+1) cos?(3x+1) Evaluate

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Q: Prove that √2+1 = 2√√(2) using √z = t²-1 et dt

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Q: Determine if the following logic is correct and explain why or why not. TC π √2-√2-12-1 √2 4 4 sinx…

A: Determine if the following logic is correct and explain why or why not. sin(x) sec(x)=1 because…

Q: verify the set {∅n = cos(nx) (∞ n=0) is orthogonal on the interval [−pi, pi]

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Q: If = {(x, y) | 16 ≤ x² + y² ≤ 49} then: 11.000 = [ co cos (x² + y²) dA

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Q: dr a) de rcose + rsene subject to r(0) = 1 (solve by separation of variables)

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Q: Which of the following is equivalent to 24 f /4- da O none of these • 12 f(1 -cos 0) dº O 24 f (1 -…

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Q: ds 1 s tan =cSC dt 2 2 2

A: We will find out the required general solution.

Q: Express the following in the form r(cos 0 + i sin 0), - < 0 ≤ π: (1 - i)(√3+ i) (1 + i)(√3-i)

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Q: Evaluate L{3e cos 10r cos 41. S+1 s+1 A. 2 (s+1) +16 (s+1) +100 S-1 S-1 B. 2 (s-1) +16 (s – 1) + 100…

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Q: Suppose &lt;let A= 1 and you know all the cofactors in C. How can you find A?

A: Given: Determinant of a matrix A  =  1 and all the co factors are known.   To find: The matrix A.

Q: e²x Prove that, (e3x+1)² fo - 8 dx 2π 9√3

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