In each of Problems 18 through 22, 3" single power series whose generic t In each of Proble ms 7 through 13, determine the Taylor series about the point xo for the given function. Also determine the radius of convergence of the series. 00 18. n(n-1) a,x-2 n -2 7. sin x, 19. xΣna,x"-1 Σ αx +Σαπ' n=1 k-0 8. ex, xo = 0 m(m - 1)am"-2 20. + x 9. x, xo = l m=2 k= 10. x2, xo = -1 21. nanx"-1 +xanx n=0 11. Inx, xo = 1 n=1 22. xn(n-1)a,x"-2+ 1 12. 1- x n=0 =2 23. Determine the a, so that the 1 13. 1 - x + nan"-1 n=1 14. Let y nx". is satisfied. Try to identify the f n=0 a. Compute y' and write out the first four terms of the series. uand write out the first four terms of the series. Σaχ. E-E

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