Question

13 1. Find a power series for the function f(x)=- centered at c=0, and 2x2 - 5x-18' determine its interval of convergence. You may use 1+x+x' +x' +. 1-X

Answer 1

fra 12 2x2 - - 18 tin) 13 2n2 + 4x-gn- 18 Zn(x+ 2)-g(n+2) fin) 13 (2+2) (2n +9) take the partial fraction of abone 13 (atz) (2009) ie A 13 (2+2) (2015) + nta zutg 13 (2+2) (eng) A (2179) + B (172) (n+2) (20+9) 13 A (2n+ 9) + 6(x+2) put na-2 we gel A(2x-2.79 ) + B (-2+2) SA A 13/5 13

put ar – 9/2 13= A (2x 9 + 9) + A(-2+2) a B = -26/5 la fint 13% - 26/5 x+2 ant g a fin - 26 5 (2019) 5 (at2) (2549 13 or fun - to (tu 26 9x5 (1+2 * fen) 26 10(1-(4) () 95 If neuf 37 - - Ian 1 I-a 120 abno beemes find 13 E (" n 26 Z } ( ² ) 10 45 nad lor font- 13 E EM (2) 26 { (2x)" nzo h2o

Date Page Z 13 En un Z 26 (18h 2 an 2n 45 ga no در ۲۱ or an? online yen in 26 24 45 gn had This is the poneer series of fen) how we know that the Radius of convergence of the power Sarles Zanah giver by nzo 나 hooo anfl an & the internal of convergent R is (-R,R) here for for fin) an (713 1 26 2h gn lu auf = lonel 26 zhel lo 2hri I guel (-100+ 13 26 - ㅟ 2h+) gnei R hyoo tin hormon 26 2n To zn gn

12 + -14 ut 2441 grel antit al 45 - 13 To in 26 2 n 455 gn 26 Ć 나 nroe genel gn 2 26 229 is gn bit 나 hao 2 Me) u how A 2. (22) 2.22m gn gn 9 = it a m nao (+) (as gre 2. o o C 4 similarly 2um goo> 4 e to goes facter to x first as nooo gn. so abone beermes ampare to go 13t lo 2 26 to = - 13 26 2 z R 2 2 to interval of convergene is (2) Answer.