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Unformatted text preview: 1) 6 ( 1 10 5 ) = 0.00001 48. error < ( 1) 4 t 4  = t 4 < 1 $ 11.7 4. lim n u n+1 u n < 1 => 1/3<x<1; when x=1/3 we have ( 1) ? n n=1 which is the alternating harmonic series and is conditionally convergent; when x=1 we have 1 n n=1 , the divergent harmonic series (a) the radius is 1/3; the interval of convergence is 1/3 =< x <1 (b) the interval of absolute convergence is 1/3< x <1 (c) the series converges conditionally at x=1/3 12. . lim n u n+1 u n < 1 => 3x lim n 1 n+1 < 1 for all x (a) the radius is ; the series converges for all x (b) the series converges absolutely for all x (c) there are no values for which the series converges conditionally 42. (a) thus the derivative of e x is e x itself (b) , which is the general antiderivative of e x (c) ; e x e x =1+0+0+0+0+0+...
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This note was uploaded on 05/27/2011 for the course ECON 201 taught by Professor Caltech during the Spring '10 term at Wisc Eau Claire.
 Spring '10
 Caltech

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