Question

a) Limits.The imits do not exist. Fo each limit fmid two arproach paths giving differet lmits Celculate the lunits along each pah. fou may Nant to use Taylor Senes expanions to simplity e limits Lim (y)-sl Cosk+ Ial+y/el PATH 1 LIMIT 1= LIMIT 2= PATH 2 b) Hamonic Funchons Recall, a fonchou f) i hamenic if it sutife the leaplace eqvahou TS the fonchou below harmonic? show yur Computahon Hoo 9)=1X+iy) W hve n is a pesihive Inkyer and i--

please help with both part a and b. Than you.

Answer 1

n (1+y)-)=(1- 7-1 Cos (x2) + V 24 2x -23 2x3 --2x 24 -2 = im LI Path 2 - 2x 4 24 - 2 im 191 7 2 24 7 umit I Pauth I -4 y=-2x2 7 Ol

n >0;Intgr. b) / プ (n+iy)n (AIntfe f n(n-) 1+iy)"-2 n-2 (n-) Ci- n2 2 ニn nl 2 n n 2 - nin-) yi)-2 -ulRi) -uu 2 7-(A -uu tor 7 ニ1. tyy - プex ニーo = i hamonuc -f) + iy" tor tyy nl1 Ingens