Question

-15 POINTS LARCALCET7M 9.8.052. Find the intervals of convergence of f(x), f'(x), F"(x), and f(x) dx. (Enter your answer using in Aw) - § (-1)+7(x – 2y (a) f(x) (b) f(x) (c) F"(x) (d) f(x) dx Need Help? Read It

Answer 1

1 + I a) f(x) = 3 t hat (x-2)? n= 1 line (anta) = lingo 1 2 - 1x-2) : series convuges if 1x-aki >-1<X-2</ 1<x<3 When 2=1, 2 & direyes When 2= 3 (nt converges - 024 ñ ... Interval of convergence = (1,3] b) 4'62) - C0"#(xv) n=2 Series converges when 1x-2/<l by geometric kacz :: Interval of in vergence = (1,3) senes

n-2 P"() Cunt (n-1)(x-2)^2 n=3 al n an = 1x-2) ! series converges if lexc3 When x= 1,3, the series divriges. ... Interval of convergence = (1/3) d) ( f(x) dx - SEDnh (X-2) + m=i (n+1) lin (ant l lim 10-2242 n(nt) no 1 an 1 x Tho+2)(x-2) 71 = lim (x-21 1 nonta = 18-21 to seves convergely tex <3 L converges When x=1,2 n(n+1) yy nanti m When x=3 SED"t1 converges Radio Interval of convergence = [1, 3]