Question

(1 point) Book Problem 15 Follow the steps below to find a power series representation for the function f(0) = ln(8 - x): a) A power series for t... (first 3 non-zero terms) - b) Observe that In(8 - 2) = | !!! dac c) The function f(x) = ln(8 - x) = +... (first 3 non-zero terms).

Answer 1

• F(x)= 118 Tica) - (1/8) - 1-(2/8) com pare - with where YE h =0 where xe(-0,8) q=118) and Y= 4/8 no no 1CM10 = 3 433"} from-E) @ 40 :13"-« *a *** ct (118) 1-(10) FX ] (3)*6*2 )+ ---- (F(2) hao Anscer First 3 non zero Terms 20 - ---- = 8-x S2 no -n= how integrare s dx = 5(3 + + +--------) dx = S2 $)"dx • INCO-W) – C+ 4x + m + ATE+ = ction ( 0 ht! inco-x) --= C+ 18 2x64 7 3X5777 +) (+1) h=0

until = ct ht enco-x) - 6t- -+---- 3x512 2x64 hD X6 at 23 To find the value of a put x=0 YO - enco) = ctotor ---- - - - ct - - ho - 5 -2.07944 = C) put value of c in eah 0 ht - ln (8-2) = -2.079 44 + x + x² + + ---=- 2:07999 x64 3X512 2 nt ntl ho now multiplied by (-ve sign both side m en co-x) = (2-01944 --za- =2-0104-Eides mit I enco-x) = 2.07944 - 1xo - 2 2x64 3X.51 = 2.07944 .-/ght hti h=0 Answer 2nd tem 3rd Herr term