Question

Integrate a power series Question Write out the first four non-zero terms of the power series representation for f(1) = In(4 + 4.c) by integrating the power series for f'. Express your answer as a sum. Sorry, that's incorrect. Try again? Basic 0

Answer 1

NOW 4+48 dhe Given flat in. (4+4x) so f(x)=de lin (4+4x)) flia- d (4+47) = 1.10+444) 4+40 f(x1= 4 4 1+2 NOW We know that formula for power segies representation of given by 1 u 4+42 142 E (-ain. ا nzo T+7 1-1-1) So NOW no so nt f(1) = 4 4 4 4 22 4 8 agn. fl(a)= 4 & Enxn .4448 Now apply integration on both sides ĕ con xndx Jf'(a) ara J et 4+48 f19)= en 14+42) = 8 Gign a tc nzo ntl f(2)= en (4+4x)= E (en ant) tc nzo nt to Now find có en (4+410))= Ž Gjn ont in 14)= orc = (c=1014) SO NOW te nti nao

f(2)= in 14+47) = in 14) + Ŝ Ena Now plug this value in o.so five in (4+4x) = Ĉ CUN nzo anti tenius 0+) nt) nt) nzo 0+1 + 0+1 2+1 f(1) = in 14+47) - en 2 41+ Giglo xº (1) 21 4 1 + 6192 g 2 + f(x1= 1114) + Å - 2 2 + 2 f(2)= en (4) + x - x2 + x3 3 3 Aue coreet But Note: your asked first four Answer es non zego teams only