Exercise 3: Let ƒ be defined on (-1,7) by [ 0, f(x) = r², 0

Exercise 3: Let ƒ be defined on (-1,7) by<br>[ 0,<br>f(x) =<br>r², 0<x < T.<br>-T <x < 0,<br>1<br>Math 4564<br>Homework Assignment<br>(a) Compute and simplify S(x) (the Fourier series of f).<br>(b) Simplify the expression of S(T). (It will involve a sum).<br>(c) Using Dirichlet's theorem, find S(7). (Hint: think about the periodic extension of f, what<br>is f(T-) and f(T+)).<br>(d) Use (b) and (c) to show that<br>1<br>+<br>1<br>+<br>+<br>16<br>1<br>+.<br>25<br>1+<br>6.<br>1=1<br>

Extracted text: Exercise 3: Let ƒ be defined on (-1,7) by [ 0, f(x) = r², 0< t.="" -t="">< 0,="" 1="" math="" 4564="" homework="" assignment="" (a)="" compute="" and="" simplify="" s(x)="" (the="" fourier="" series="" of="" f).="" (b)="" simplify="" the="" expression="" of="" s(t).="" (it="" will="" involve="" a="" sum).="" (c)="" using="" dirichlet's="" theorem,="" find="" s(7).="" (hint:="" think="" about="" the="" periodic="" extension="" of="" f,="" what="" is="" f(t-)="" and="" f(t+)).="" (d)="" use="" (b)="" and="" (c)="" to="" show="" that="" 1="" +="" 1="" +="" +="" 16="" 1="" +.="" 25="" 1+="" 6.="" 1="">

Jun 05, 2022

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Exercise 3: Let ƒ be defined on (-1,7) by [ 0, f(x) = r², 0

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