Question

number 3a and 4a

3 Reprenent The eti an Of coaurgane a radias of omvengeure uer aarieynd The intmuel Cas fixs , C fx)2 () fix 3 Ix2 -x fin3ta e Fix ) )2 I-) (9) fィ)= In C+x2) dirge Detan it he seria, conng abioht/y, caud>tioully ノロr (A) C- kro k! d) ;(e) kEI k Vh (4)E

Answer 1

f (x)=2 4+x 440 f(a) 2u 2 2 =- 2 (4+0)3 (4+x)2 42 2 ニ-2 - (4+x)3 f"(a)1 - +2. 2 - *(t) = 2.2 4+0) 3 2 (xth) continuiny and So f"(o) t2. n =-12. nti By Maclaurin of fw series fizi= (0).2 2. 442 X Zniz nt2 ntl (22)n* o u Oo n -1 2n+ och Lit an x an =(-1 22n+i (-1) anti Ant 3 2 M8MM&

Radius of Convery ene, Re it an anti 22n+3 (-1n41 1 X 22nt! 1221 t So, Series at 2n n 2n 22n+1 2 nao 2. 2 is altennating Sunies where an 2. which As t an t0. So it diverges 2 2 Oo 22 00 at 24 1 2 M-O 22 クニ。227イi X 47 () 1 ±0. an =lt an-1 again 2 di verges. 2 Thus, interval ef 2e (-4,4) ey lonverjence is

4(a) (-1)3 kI ak ヒ=0 ao if Slar Comverges. Cenveryes absolutely New マニオ 3 3 (meN larl= 1 K! ロニオ C3 &CKTI CE3 (k+リ! CE+I K! Thurs (kt1)! koo KI t t (Kt). K! lar Converges by Hatio-test hence, feo ヒ=0 kr 00 EINK 3 onvenges abilutely Sa Co K! M M M -18