Question

(1 point) - 2x² Find the Maclaurin series for the function f(x) = r the function (x) = - 2 in the form (f(x) = n=0 Notice if a coefficient requested below is missing in the series then that coefficient is zero and you should enter 0. Find the individual coefficients Now give the general term as a formula involving n C. =

Answer 1

solution: f(x) = 272 1-32 We know, to ta= 1+x+x2 + x3 +...+x"+o. :. =1+34 + (3x)² + (3x) + - 1-30 + 32)"+... 2x2 2 1-32 = 2062 + 2.323+2-32204 2.33.5+ ... +237 27+2 to- Į 2.3m ante 120 : C-a, ci = 67, 6 =21,3 =6), (4=118 cs=154] fog

2x² - = 2x^4 2 3x3 + 2.3 ++ 2.345 4... + 2-3px)+. 1-301 t... Co = O co C2 = [2] <s = [54 ] 54 .. f(a) = 222 co z 2-39 2n+2 na@o = Ž 2:3h-zyn 1-32 n =2 a cn = 2.30-2