Question

13 . Find a power series for the function f(x)= centered at c=0, and 2x’ - 5x-18' determine its interval of convergence. You may use 1+x+ x² + x +. 1-X

Answer 1

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Answer 2

solution The Power series fore the function centested at ezo. f(n) 13 2 22-50-18 {ca) 13 2(x-9²-5(0-0) - 18 11 13 I 22-54-18 13 = म 2x 9x +42-18 13 - 1) 2 27-9 2+2 229 2 (2x–9.)(x+2) ta Fare 2 Ž 4 ) 1+x+2+ --- 은 - at n I-X = dlo le x = if 1441 hao 1-a no n = () (2 fore, 272 td (1+2 @ 3) n I+x+*+- tx Licenta fim il n 3 = x nzo an St nal Frcom@, ta)= - - CE G)"}* whien of the reequired power series for the function f(n) is centeich ateso, hao -13 2x 54-18

The interval of Connergence of given by 272 " L1 | 2714 i-e, -1 - a 221 ire, La La : The interval of convergence of @ I. (-4, 9) Fore the internal of convergence of B b 1-2 / 니 ice, 1 - XLI on, 17 27-1 -1LZL on, on, -22X22 + The internal of convergence of b fz (-2, 2) The common reegion of f f ff in (-2,2) for convergence The required internal of the function f(n) (-2,2). ... 13 2x-50-18

solution The Power series fore the function centested at ezo. f(n) 13 2 22-50-18 {ca) 13 2(x-9²-5(0-0) - 18 11 13 I 22-54-18 13 = म 2x 9x +42-18 13 - 1) 2 27-9 2+2 229 2 (2x–9.)(x+2) ta Fare 2 Ž 4 ) 1+x+2+ --- 은 - at n I-X = 3 le x = if 1441 hao 1-a no n = () (2 fore, 272 td (1+2 @ 3) n I+x+*+- tx Licenta fim il n 3 = x nzo an St nal Frcom@, ta)= - - CE G)"}* whien of the reequired power series for the function f(n) is centeich ateso, hao -13 2x 54-18