Question

Use a contour to evaluate S (2-1)723 +1) da 7T Answer:

Answer 1

# Am! I= 8 9 20249 da 736-1)(3341) 0 2 ²422 let fr) = C-1)(734) poles of free where as +1+1'13 9 given by: (2-1)(4340)20 +7=1,-1, a, a as 23+= (CH2(22-2+)) a = I- 2 6 c S.L ; R) to 2.2422 3 ZAI ZAI 234 2 Consider closed Contour C = [-R, RJ U Ck U GUCI 4 upper half past of Circle leler Obuvoilly *+, a lies in Cand we remoue 151 Singularity Now by by inclentahune. Residue themem Je faide (21120) Res (f(x); << t !, al (*) Res [fcri, e=1 lim (2-1) f(e) = lim Res [fon, Z=-1 E' lim (zh).fer) = lim 2427 2--| 2011 (2-1) (ZZZ+1) Res [feer; t-a] - lim (za) fresa lim Ş Z2472 tel 2-4 1(2-1)(CHL)(z-a) d24ad (²1) cara ) Note: Cl2 = (1+1 3 2 - 1713 (1-3 +213) I til artza THEG ) = (1+315) 2 dr_1 THER % (-3 + 3). a-a Scanned with (=$115) (implify by Calculation } +1 6 اری رہی سن + 2 (iteta Chesteforeneri

Since a -R 1 -0-1 1 48'R 0 -R 471 71 + IR . faida R 121² 2121 1d2l C = (-R,=>JU CIUTAT, I-81) UC 01148!,p] UCH Hence by Resurclu theorem Conle only pole de tik liel liel in c) Sefaride (212') [ Res (fc21,2-01) + fonde + Szufride + Sam Hauscles Si me fazo dz +Scafczıdz =(291) (-5--13) - S + Win (4) letfizidels Seat fecalledel € Sed Scot le=Rai = Reid (R-1)Ć R3-1) s for C[+!p) (1-YR) (1–Yp3) due to the to Scat fczdz = 0 -19116 ) fis) flim (2+0 fab = lig. Seit fcende = Ein) {fym (712.fc23} = - 31st (@r) in (*), s me 1,0,0 New také limiy rto, &)0 R-) Se founds +(-Bron) +S" founda + (-ig)+1, Hand u to = *+24 Götfit, u fondo = (loze' – ) +3855 ca faning om fonds < R2+QR lath12 141-161 ide 7 dz: iRecce It R do O as RO (IN ces lanco €) zo lim Set foz, de - 2-)-1 2-) 1 3723