5331088930

<£ £ldz=p— dz......(2)

J?12 2    ix J 2

^{(sub stitu te}'⁼‘^z)=ę ^ <-*>⁼c    ⁼c v*......^<3)

r e‘

lim t —dz = O (By Jordan lemma)......(4)

*j-»® J »2 ^

«    0 o’*¹**    0

lim £ —c/z = lim I —rHie^fdd (Substitute z =/?,e^f ) = lim I /'e'*^;C*d0=[/'0]° =-ix ......(5)

S.-fOJyl i    *.-»0Jt    ¹    *.-*0Jx

lim [f ‘ — dz + f ‘-dz+O+(-/*)] = 0 (Substitute (2), (3), (4), (5) into (1))

z    ^{J ?}s    Z

*.-»o

rs₂ e^:    f*.

lim ([ ‘ — dz + [ ‘—dz)=ix

*,-»0

■tx

lim (f — dz-f ——dz)=//

s.-*o

lim    ^e'~^e-dz = -

2/z    2

*.-»o

lim p*5£*-'

r = sinz , z -dz = —

Jo    z    2