EGM4313HW12 - Page 679, problem 16: (20 30i ) n 1 n ! lim n...

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Page 679, problem 16: 1 (20 30 ) ! 20 30 lim lim 0 1 (20 30 ) ( 1)! 1 n n nn i n i i n n converges Page 679, problem 24 An important limit: 1 lim(1 ) n n e n Find this by taking the limit 1 ln(1 ) 11 limln((1 ) ) lim ln(1 ) lim 1 n n n n n n n Use L’Hopital’s Rule: 2 2 1 lim lim 1 lim(1 ) 1 1 1 (1 )( ) 1 n n n n n e n n n n 1 1 (3 ) ( 1)! 3 3 lim lim 1 1 (3 ) !( 1) ) n i n n i i n n e n diverges Page 684, problem 8: 0 zi 1 ( ! 1 lim lim( ) ( 1)! n n n n n n e n n n Therefore the radius of convergence is 1 R e Page 684, problem 13: 0
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1 4 4 4 4 4 16 ( ) 1 1 lim lim 16( ) 1 16 ( ) 2 16 nn zi z i z i Page 689, problem 6: (a) 1 23 2 2 2 21 ( 1) () 2 3 2 lim lim ( ) 1 2 ( 1) 2 3 2 4 2 1 2 n n n n z z nz n z z n n (b) 22 2 1 2 2 2 ( 1) 2 lim lim ( ) 1 2 ( 1) 2 4 2 n n n n z z z z z Page 697, problem 5: 4 8 12 4 4 4 8 12 4 4 1 1 1 1 ( ) (1 ) 2 2 2 2 4 8 1 ( ) 2 1 2 4 8 16 12 2 z z z fz z z z z z z z Page 697, problem 18 ( ) ( ) 11 1 0 2 1 ( 1) ! ( 1) ! ( ) ( ) ( ) ( 1) ( ) ( ) ( 1) lim 1 ( 1)
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This note was uploaded on 12/15/2011 for the course EGM 4313 taught by Professor Mei during the Fall '08 term at University of Florida.

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EGM4313HW12 - Page 679, problem 16: (20 30i ) n 1 n ! lim n...

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