10. (a) Find the Fourier series for the function ƒ: R → R determined by ƒ(x): x² for x = [−π, π] and ƒ(x + 2π) = f(x) for all x = R and using facts considered in lecture, explain why the Fourier series coverges to f(x) at each point x = (-π, πT). = (b) Using the Fourier series representation from part (a), evaluate ∞ (−1)n n² n=1

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A: Your expression of series is typing mistake, it should be 1/(2n-1)².

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A: Graph of the function and it's series

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A: The Fourier series of given function is given as follows

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Q: Consider the piecewise function x, -2 0. (v) Find the simplified general expression for the Fourier…

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A: Given:

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Q: 2. (a) Find Fourier Series representation of the function with period 2 defined by f(t)=sin (1/2).

A: Sol:- Fourier series of function fx on interval -L≤ x≤ L is defined as: x=A0+∑n=1∞ An·cosnπxL+∑n=1∞…

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A: The solution is given as

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