For the following function, you are given one period of the function. f(x) = sin tx on the interval - < x < For this function, complete the following tasks: A. Sketch several periods of the funcion B. Expand it in a sine-cosine Fourier Series. C. Expand it in a complex exponential Fourier Series.

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

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A: Note: As per our guidelines, we can solve first question. Please repost the remaining questions.

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A: We recall Gauss's Lemma and using Gauss Lemma we solve the problem.

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A: By using given definition of Laplace transform, we will find the Laplace of the given function.

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A: According to our guidelines we can solve only first three subparts.Kindly repost remaining subpart.

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A: The given trigonometric equation .The aim is to find the solutions to the given equation.

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Q: 9. Let G be a group of order 255. Show that (1) Sylow 17-subgroup is normal in G. (ii) 3 a normal…

A: According to guidelines we can solve only first three subparts, please repost other separately.

Q: What are the solutions to the equation ? A nment 4 y = 15x + 1 3 2 AUGAS2 수 y = x + 1 2 3

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

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A: Since, all automobile license plates have three uppercase letters followed by three digits.Total…

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Q: 2. Solve the integro-differential equation for f(t) t –2f(t) = 2 | sinh(w)f(t – w)dw + 1 2 f'sir

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A: We have to find the missing coordinates of orthonormal basis.

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Q: 6. Let V be a finite-dimensional vector space and E a subspace. Prove that V = EE¹.

A: To prove that V=E⊕E⊥,  need to show two things:1. V=E+E⊥ (the sum of E and E⊥ spans V),2. E∩E⊥={0}…

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