Determine the Fourier Series of f(x) = x², over the interval - < x < and has period 2 O! f(x) = [ cos x + cos 3x + cos 5x + ] [₁ sina+sin 2x + sin 3x +... ·] 2 1 1 f(x) sina+sin 3x + sin 5x +.. 1 ㅠ 3 O # 1 f(x) -{sina+sin 2x + si ..... 2 3 $ 1 f(2)=-4 cos z - cos 2z+cos 3r - cos 4r +. 1 22 3x 4x J 3 4² = 3π = 4 1 2 2 sin 3x +

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A: Introduction :

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A: Since there are multiple questions posted, we will answer the first question posted (4). If you want…

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A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

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A: This is related to Complex Analysis

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A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

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Q: what is the fourier series of f(t)=e^abs(t) -pi<t<pi

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A: Given that, y(x)=∂2∂x∂zz2x+cosx44cosh2x-sinh2x16cos2πxddx(2x2) This can be rewritten as,…

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A: Given: To calculate  y'' + 2y' Here,  y(x) = ∂2∂x∂zz2x + coz x4 4 (cosh 2x - sinh 2x)16cos 2π xddx…

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A: Between any two real roots there is a one root of its derivative.

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A: The objective is to find the derivative of f(x).

Q: Prove that, Cosh(A+B) = CoshACoshB + SinhASinhB. Deduce a similar expression for Sinh(A+B)

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A: We will find out the required solution.