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Problem 4. Let 0<4 g(r) ecos (a) write the Fourier cosine series and the Fourier sine series respectively. (b) Draw the graph

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Answer #1

a)

Then Pouries CoSing Sies Zanon e 4 t(-CeST (E) a)asltE 1 -asdtetas(9-)ad 1-eot (m+) -C (n- -I 2+ 24 1+ e- 1e 4Poue aSlme geries 19 hen ty +e Mt Noco Fouer Sme serees to t alere lethtte( eengtDatt tsm/4-0m1]4t e t + 4(-re -ne H(D (+D(1-Therefore the fourier sine series of g is:

(1-)T ii(+-)

b)

-2 2

fourier cosine series is better than fourier sine series because fourier cosine series is uniformly convergent which can be proved by weitrass but we dont know fourier series is uniformly convergent or not

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