Lecture41-rev

Lecture41-rev - ! rp Y f(x) 1 2 a1 a2 ... ... n n+1 an...

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Unformatted text preview: ! rp Y f(x) 1 2 a1 a2 ... ... n n+1 an upper sum N aN-1 x z p w wu u Tw6 w u`p ~ w u e u u u} 76 6 7 94 % 3 &E# 2 % 8 u yw yvTw6 w w u xw|{ z 6 u çw6 uQp ~ w u u wcu u w qyw e|{ u w w p u H 6 4 % 3 &%E# 6 8 7 94 2 6 4 6 w 6 AA4 d 76 76 4 4 AA4 76 6 % 2 y &7# % 4 4 8 6 6 6 % 2 y &%7# e 8 e '~ ~ %v ~ p c z 6 ( z ! u G ~ }u |{ v u ~ wu 6 w 2 u Gq ~ H 7u Gc % 3 &%7# 8 w q6 u 6 G@ ~ u G G~ 6 ~ 7 6 ~ ! 7u 6 ~ % 3 1%E# 8 6 6 2 u |{ u 6 H 6 7 % 3 1E# 2 % 6 8 % 2 y &%E# H 6 8 4AA4 % 2 y &%E# d 8 % 2 y 1%E# d 8 6 AA4 d 4 4 4 H 6 6 2 y e H 6 % 1%E# e 8 H 6 H 6 u Gqw ! ~ ! v ~ p 'Tc wvv % 23 &%7# s 8 e Gsu z ! qpw u Gc w ! w pw u 6G G~ u yxw6 u u u |{ z ! w qp ~ pw u u $uQqTvywu ~ u w w w r ! ! r ! r ! H yvyw H % vyw % 2 H % 8 yvw % 2 H % 8 ~ z c u u ~u x U w s 6 w# H H % &%e # Gww G'u y# u|{ z vy ! ' G~ 6 H % &%E# d b z !f & i u~ w tuTv uu u B ! ~ p u Gq u w6 u u 2 w 74Deihh'% w ~ z c r r Y Y u w u uUp ~ 6 GqB ~ 6 G~ u2 Txv6S w w ! ...
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This note was uploaded on 03/04/2012 for the course MATH 10250 taught by Professor Himonas during the Fall '08 term at Notre Dame.

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