Question

2x-1= 0 11. Find the radius of convergence of 112. 3(x+1) (x+2 (Intllip Int 3/16 12. Find the Maclaurin series for f(x) = showing how you got it. Plx) = ax flo)=4 u

Answer 1

so 3M (x+2) , anfo and / sol (n+j)3 SERIES Ratio Test if there exists an n so that for all new Lim hayo lant! 1.22 if Lal, Then Ean converges if L>l, Then Elan diverges if Lal, then the test is incon clogine an 3 i E 3 (x+2) (n+D3 (272)3 Lim ra niso L 36842) Cat33 11 LT672331 = 13 (x2)). Lim M+)3 , nooo m+2)3 | - 3leto) 1 = 31x+2) The som converges for Lal, therefore gone. 31x+2) <1 7 lxt2l <Y3... * Apply Absolute rule if lisca, aso. Then -acuca - - -1/3 <x+ 2CY. X+2>-13 and X+2<\/3.

8 . x>-713 and X<-513 : combine the intervals xx-713 and xx-513 merge overlapping intervals -7135*5-313. The sum may converge for 2=1 Therefore check convergene for 3lx+21 =1 por x=-73 {oan ((-73)+2)" (n+133 converses cabsontey Boxes 7135X<-5/3 · For x= -5/3, 3" ((-5/3) +2)" n=0 67103 Converty 7/35X2-5/3 rading of Conrqué.. o 1. Ooop: /exsasbl