Question

X=0. 2x b f(x) = (x - 1)? 3) Find the power Series representation for f(x) around Also specify the set of convergence. a) f(x) (1+x2 c) f(x) = fan'cx) e) f(x) = x = x Cao3x – 54 x) d) f(x) = VI 777?

Please solve all I will rate

Answer 1

for ftae Powen series representation ㅗ about aro ch 109 (1+x)2 2 If nxt nona 2x + know that (!+se)" (1+x) I unat ninti) x2 21 non ho for 1 21st = 1 - 202 + 3*24+$24 for 121) Now رها for 121131 (-19” (ion) Σ tim un un un+1 nth term (21) nutn) (-1^t! (+02 u n +1 lim R = Wn+/ is lal LR bence Intervel of convergence at C-1,1) at Ha!, -1 is divergent E Encan) the servies since at x=1 div. / n-D at Elitn) div. nco 2 X line) 2x 2 f(x) 22 (I-1) 12 2 3 for lar</ n 27 + + 226 ++372 +421 [v+23+37? لا -) 2x + 4 4 4 6 4 2 + 8 + 9 + = ) for { x? an Inici n1 Interival won ✓ given re(-1,1)

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