Question

2) Given that 4 cos[(2n + 1)x] |x| = = = - - nao ,- < x <te. (2n + 1)2 Find the Fourier series of g(x) = -1 1 -1 < x < 0 0 < x <TE 1

Answer 1

1701 to [ $? 4 Comment y We canon 7 ans H udinna +5 ° sin pa din + x dinnn " - )" sin pour 9 on #1 044-71) Sin cana) (mm) en -- no Onni ne h osny + T sinni-ot/ n ( h2 I finna - Cest-HT) +11 sinni 12 n na / he]] 2 7 + GNTTI a an= 1 an sin nit m2 + Gentil + ona An= til ny fan] [~ Sinntino) an= a [64] u n-odel (VI) alan= AT neuen neuen find buit Hul din nudu ban 7 Install ºn sinunda + "vinnudn) IT

- 77 fins is an even tunchion 41-4)= Huy and "Sin nu? is odel tunition Result- fuidu= 0 if Hus is odel function. 7 / "Atul din urdu-o & Poncol (1x) None foueres Socies of Huis is given by Hu) = 40 + (an cosnu+by Sinnn) 7 dni = t. 8 2 1 (+124] Casnn . 7 Sm= + (691_7 Goma & sn= It / Ecold he can na - 2 osnu c los (antin +/sw- I - Hoo non Cantina TRARTE Hence, the Prost.

- 77 fins is an even tunchion 41-4)= Huy and "Sin nu? is odel tunition Result- fuidu= 0 if Hus is odel function. 7 / "Atul din urdu-o & Poncol (1x) None foueres Socies of Huis is given by Hu) = 40 + (an cosnu+by Sinnn) 7 dni = t. 8 2 1 (+124] Casnn . 7 Sm= + (691_7 Goma & sn= It / Ecold he can na - 2 osnu c los (antin +/sw- I - Hoo non Cantina TRARTE Hence, the Prost.

70 !n comendo a "honnan VE TEST ne ne aan # 0+1-T) din(na) - sammen med + TT binne-o + a contenu a on=tltl linna - 1 (:) + TI ding + Gnatate a an= #1 at finna - 1 12+ Grid & Gen 1 he] tan = tol ] . Sinnaco] on = henta (0)4] le n=odel - (Vill) n=euen find bn bn=ts Jus din nude Inc+ 1 ulinnudu + Ty din nudin

w We fenene that foverer Series is given by.£m [cic+an] Jem) = 2e + Ž (an Coon + bn din nu) - na to o where ctati u No=. - s fluidh O ctall ) Un= 1 + 1 Heu. Cesnudu (n=11213 bnat flue-finnudu , (n=114121 - all Where, where au jan and bn are called towel coeficient dol of ofl. od -T LUKO hinen, wa | OSUCTI them fomijez Series of gows is given by olm = 99 + Žlan bunu+ bn finna) |_in] first we find ao, an and b 14 Find 0-7 90 = + 1 gunder ** 14 can try "omg to | EML +()0") + [+1+12 [a=0 (11)

and only one tag on windows Un * * .* annda t { "cum den 9 H1 ( simple int ( sangang mag-isa ++/ -dinna + finna -o] ☆ Ton zo] +130 cm fined in I gius fin nudu = + 1 ! Um einn du 1 rn Bonudbo + bu=+1 ta cómundu + "binnen on=#1 Banyoles #bn= */ 1–69 () _ (6917-447. + bn = ta I to - Gina - Gumi th] * a bnat l ñ i Gorning

I'N bn= 1 & 2 and] bne hill-om) =) on enn 11-] [bna n-odel 10 neven n=euen 10 na n여 Ubing (1927), QUI and () in (1.9, we get gim) = 4 + lan Gunu+bn Sinnu) glu)= 0 + ² (0. Osnu + bn finna) a glu) = { Insinnn 껴 & glas o 4 dinn to Sinan + y sinont- & (ginin u finn + y sinont u dinsnt- Ishich is the required tourier Series of gluj, 101 fo Bârgqv iera 49mS