# assignment_sheet_WA09A_MAT-232-GS.rtf - Written Assignment...

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Written Assignment 9Answer all assigned exercises, and show all work. Each exercise is worth 10 points.*Submitting a graph is not required; however, you are encouraged to create one for your own benefit and to include (or describe) one if possible.Section 8.62.Determine the radius and interval of convergence.03!kkkxk01111113!311!3!33!311!limlim.lim3 lim031!311!kkkkknkknkkkkkkkkkkkkxkxakaxkxkxkxxkxkkxkTherefore 03!kkkxkconverges absolutely for x (-∞, ∞); r=∞4.Determine the radius and interval of convergence.02kkkkxWA 9, p. 1
011111112122112(1)12limlim.limlim2222212;12;2222kkkkknknkkkkkkkkkkkkkkxkxakaxkxkxx kxkxkkxkkxxxxxx Therefore 02kkkkxconverges absolutely for x (-2, 2); r=28.Determine the radius and interval of convergence.2111(1)kkxk2112312_1232222_121(1)1111lim1lim1(1)111111110112kkkkkkkkkkxkxkaaxkxkkxxxConvergeskxkxxxxx When -1<x-1<1 then 0<x<2Therefore 2111(1)kkxkconverges absolutely (0, 2); r=110.Determine the radius and interval of convergence.WA 9, p. 2
241(32)kkxk241211221222222221(32)1321323232.1(32)111(32)32lim32 lim32113213213113321331kkkkknkknkkxkxkxxkxakaxkkkxkkxkxxConvergeskkxxxxxxx     When -1<3x+2<1 then 113x  Therefore 241(32)kkxkconverges (-1, 13); r=13WA 9, p. 3
12.Determine the radius and interval of convergence.1( 1)(31)kkkxk1111( 1)(31)1(31)(31)1( 1)1(31)(31)lim31 lim311131131132233110kkkkknkknkkxkxakxkakxkkxkxxConvergeskkxxxxxx   When -1<3x-1<1 then 203xTherefore 1( 1)(31)kkkxkconverges (0, 23); r=13WA 9, p. 4
16.Determine the radius and interval of convergence.2212( !)(2 )!kkkxk   2212221122211212221212222222212( !)(2 )!(1!)1 !(1!)(2 )!(21)!.( !)(21)!( !)2 !121(2 )!1 !1 !1limlim.2 !1212!121222( !)22(2 )!kkkknkknkkkkkkxkkxxkakxkkkakkxkkkxkxkkxxkkkkkkxkk1222122221221222122( !)(2 )!2( !)lim(2 )!2( !)2( !)2(2 )!(2 )!2( !)lim(2 )!kkkkkkkkkkkkkkDivergeskxkkkkkDivergesk     Therefore 2212( !)(2 )!kkkxkconverges for -2<x<2 and diverges x<-2 or x>2(-2, 2); r=220.Determine the interval of convergence and the function to which the given power series converges.0(3)kkxWA 9, p. 5
011(3)(3)3314312kkknknxaxxxxxx Therefore 0(3)kkxconverges for 24x(2, 4); r=124.Determine the interval of convergence and the function to which the given power series converges.034kkx0113434434limlim 1444144144kkknknkkxxaxaxxxxxxxx  Therefore 034kkxconverges for 44x(-4, 4); r=426.Find a power series representation of f(x)about c= 0(refer to example 6.6). Also, determine the radius and interval of convergence, and graph f(x)together with the partial sums 30kkka xand 60kkka x.