Question

19.

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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = e-3x f(x) = Σ n = 0 Find the associated radius of convergence R. R =

20

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21

Answer 1

31 fa)= 36) = 1 given function fo) = do) -31 5.3 -38 (9) aseo S • ce) + g) - A)63) : 1 - 23:31 {"s) : 3-23g) 8 2 =9 % }} 1.0 - 8) 8) (-1) :1 4 - - ???? 2 33-3(e) 1 - - 31-23 C fillon 그 - Pow) Mac lauren series ft) te) ff log a t" * + {) tt พ Y d) 2 flag ๆ .. 1 + Es) จ 1! t63) 3 ic 1) 1 2 - (@f ( - ? 4 + B32 t 11 รณร - 2} 3 ) f(x7 - 1 (23 no */ (762) here radiocy of convergence -1291 ( LY L you รๆ 2. /3 Radies of Convergence{(-1/3, 43)} 22 R - V2

وي طبع کے باره ی ما - - fr ) zona +1502 ens 2 (eg Hernah movie ك) )۱+) = و - در = ( ۱۱ ل = (مام +6) - Vs لة 늦 7 % 2 مر) ة 띁 و 2 - 2 fillon 3. 3. دربی به - series Tay las الاحلام د- دام + دو- م 2ماه ۴- 62 2 2 م ہے اه (5) (4) 3 117 م 1 = ة و با مه ر 44 + ( 4 + (46 = 89 2 3) 14 + 2. line) 23 ( ه - (2-1) (1-2) با + إ2 ہے ج# ۱۱ + , 53 ع ع ع ورا + کر لیا۔ ار ده استم ) ہوا ۔ م ) في 27 م 3 43 را 3 : + رسم

f) = ln(5) ts u=1 froņ+1 eyn n Radious of convergence more lars 125 scarsas +5+5 Lacsos cncio 30.10/3.10.2010 10-025 Redious of convergente Ras

21 - L ) 세4 Sionomiad expansion 마다 기니 개 2 +끼가기 nnes ) n2 옥에 Au-1 = 고 uk) 다. 2 14 m2 + 사위부 4 2-1= 1-14 기3 다 } 다. 법에 3기와 아들기 킬름 쫰 +) t + I 23 1 3)

= 1 - 1 21-г 4- 2 +37 73 3 3) + c (-) 1+1 1 - 1 E И-9 — - 12-р Ч. 2. су - uy ---- E- ieouta is correct one one opti