evaluate the following integrals. please show procedure. Develop g(z)= 1/(z-1)(z-2) into a laurent series that is...
evaluate the following integrals. delvelop h(z)= z/((z+1)(z-1)) into a laurent series, in the followinf domains. 7) s r=4121 = { Y 2z-1 dz z?(??+1) de | +į sene - 8) 5" Sol: 40 2T 9) COS O de 3 tsen o O ) 0 ( 2 + 1 / 3 3ے 21- او(ح1
please answer its urgent. develop f(z)=(z(z-3)) into a laurent serkes valid for the following domains develop g(z)= 1/((z-1)(z-2)) into a laurent series valid for the following domains develop h(z)= z/((z+1)(z-2)) into a laurent series valid for the following domains 7) 0 < 1 2 -3/ <3 6) 1८11-4/<4 9) 0시레시 10) 0<l2-2시 ) ۵ < ( 2 + ( ( 3 (2) 02 ( 2 -2) 3.
Develop f(z)=1/(z(z-3)) in a laurent series valid for the indicated domains. determine the nature of the singularities of the following functions. 0시리 <3 6) 3<시리 22 13) f(3) = -1 14) FCZ) = sen (42) - 42 Z 22
evaluate the following integrals in the given regions. 5) S 37 + 1 2(2-2)2 dz r 2 6)S piz (z²+1)? dz I Y
= t a r has a Laurent series representation about the 2. Show that f(s) = point = = i given by ř (1 - i)n-1 f(3) = (valid for 12-il > V2).
exercise 4 please 1. Expand the function in a Laurent series that converges for 0 < [z] <R and determine the precise region of convergence. Show details. a. zz-1) (10%) 72-73 (10%) ez b. 2. Determine the location and order of the zeros. a. sin 2 (10%) b. coshºz (10%) 3. Residue integration a. Dedz,c: [2] = a (15%) b. $ 273dz,c: [2] => (15%) 4. Evaluate the following integrals. Show details. a. Lorem (15%) b. Lo**ay (15%)
2-1/2dz if C is a polygonal line with vertices 2,1 + i,-1 i,-2 (without the segment [-2,2) and z-1/ is a principal value. Hint: consider a particular branch which is analytic on the contour uate the following integrals (all contours are positively oriented): cosh(z) 3 dz if C is a square of vertices 1 ti,-1ti C 2 sin(2) dz if C is a circle 3 2(2,2 2 3 dz if C is a rectangle with sides along the lines x-1,x--1,y...
Evaluate each of the following integrals Z 2z Je cos dz i. 4/ (Xcos (4x)dx 2 ii. t'sin 2t dt ii Sy°cos 3ydy iv. 14x3-9х*+7х+3)е*dx- 2 V.
1 9. Expand f(z) = (2-1)-(2-6) as a Laurent series a) for 12-11 > R. R=? (Note: Pay attention, it is for >R, NOT <R.) b) for 12 - 41 <K. K=?
use residue theorem to evaluate the following integrals sin z 21) 20) Cosx dx (r? + 1) X 22) sin mx dx 2(x² + a²² (a > 0, b>0) 23) cos ex - cos bx -dx x?