Question

asist mates fx) with an error of at most 0.1. G. Find the Fourier series for sinh x. Prove that this series does not converge uniformly for Find a number N such that the partial sum sw(x) of the Fourier series for f(x) = \x/ approxi- Show that if p(x) > 0 for -- SXS, (x)f(x)f*(x) dx s {for-dx}" {{ogv=dx}" mugh that the right hand side is finite

3 or 4 plz
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Answer 1

-E 4 Costa) 2 hrodd The fius = 7 4 losu لا Costu Cos3K + t. + -] 2 12 32 52 12 1 32 ta -7 KE 0, f0)=- 4 [++*+++ ] =-4 [+ 7- (********* say that this seriessari convergent series 1 * | So, we can sa Anw

-E 4 Costa) 2 hrodd The fius = 7 4 losu لا Costu Cos3K + t. + -] 2 12 32 52 12 1 32 ta -7 KE 0, f0)=- 4 [++*+++ ] =-4 [+ 7- (********* say that this seriessari convergent series 1 * | So, we can sa Anw

Tifowdx solution - f(x) = lxl Y = 11 . W can see in figure Ixlis even function so we can say bntor 1 Sifi) Sinnx dx ,n21, : symetric about y-aviy ** w tanow forien series- fres=90+ E an Cosmx2 + E bn Sin (mm) o +TT ון 2 n=1 N=1 9. TT - Et xdre = fredes ndr = 1 NOW, 1 2n = + S fluCos (nm)dx. - 2 •T x Cos (na odre Sh IT so - ? [x sin (nu) - - (1. Sininauda [xsinni + losun h2 2 [cas enn i n o Th² -4 Th² neodd Nzeven inz [c4094 J = "So, Fourier series is write by fCXC) = an Cosw) to 90 2 + E n=odd 11 +E - y Cosna th No add
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