Question

a Using f2) = e T42/22-1, show that noo cos CTTx/2) doc --T -00 JC2 | abc = -1 Ob Shad that to ex ebx (se - [cot (92) - Cat (67)] Hat eak Use a FR, TI) I-ex as rectangular conform with vernces at C-R,O) RO) and R, IT) with a Seme Carcle indentation at the origin.

Answer 1

Answer: z - 2 2 - 1 Z +1 HF272 Is It Iz I. ITZ/2 / dz dt = z =) =-I is a z-1 pole. / Z +1 I u ca nu are the one Cauchi n! ( fiz) to Pole Cauches form. ZH J (z-zo) ntl I Here f(t)= e 12 f(-1) = e(a) -1-1 Iz - 20 = tz-1) dz = if (zo) I wi.it 24 = 2tifead) E-T.

US e ax e di - da &- $ het ex =+ = I dt n=- =0 do ta o = III Iz & for that (1-4) dt - ( + (1-6) de P (8,4)= 0.00 *= (1+0) %* at II- (- (tjal (1+ (-1)-a-cira) at = (-ja-l B (and, 1-a) x=a ,-X-4 =-1 = "=1-a Similarly I2 = Eubul B (b, 1-b)

I = I1 - 12 = (-1) 9-18 (a, 1-2) - (-1) 2 B (by + b) = (-1)rca)r (1-a) - (Dr (br (16) = (-1) rb 2 Sincast) sin(st) = T ( Coslan - Costot) ) sincat sin (bit) = * (cotlant) - Lot (b)). I sin (1x) = 1 1 1 1 =) -ar(a)(-a) - T Sin catt) r(a) xr (« l-a) = TT ✓ or sin (at)