Find the Fourier transform of f(x) = cos 2x in the sense of the Fourier transform of distributions. Hint: Use Euler's formula eia +e-ia 2 and the formula for the inverse Fourier transform. cos a =

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Q: method: Question 4. Solve the following initial value problem using Laplace transform y" + 4y' + 13y…

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Q: Let Let L: R³ → R³ be the linear transformation defined by [4] = B = C = -4 L(x) = -1 2 -3 -3 3 -2…

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Q: Find the Inverse Laplace transform of : 5s-2 s² (s+2) (S-1) a) b) S (s²+a²)(s²+b²)' a² # b², ab # 0

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Q: ne Zt. Solve the congruence x = n" (mod p), where p is a prime of the form 4n ± 1,

A: To solve : The congruence x ≡ nn mod p , where p is a prime of the form 4n ± 1 , n ∈ ℤ+ .

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Q: 2. Find all the square roots of 9 in Zi04.

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