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由 cloudsea 於 星期一 二月 27, 2006 12:44 am
請問一下樓上的大大...如果今天改為正實數可積...那是不是在無限大跟負無限大都定義為F(x) = 0 for x -> 無限大 and F(x) = 0 for x -> 負無限大 ? #ed_op#BR#ed_cl#希望幫忙解惑...謝謝... 還有就是 for x =1 時 , F(x) = sin(1) 嗎 ? #ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#
由 訪客 於 星期日 二月 26, 2006 2:26 pm
#ed_op#DIV#ed_cl#f(x) = (sinx)/x for x in (0,1)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#令#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#F(x)=1 for x=0 #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#F(x)=(sinx)/x for x in (0,1)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#F(x)=sinx1 for x=1#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#則#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#F(x) 在[0,1]為連續函數,所以F(x)在[0,1]為可積#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#所以 F(x)在(0,1)亦為可知#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#所以f(x)在(0,1)可積#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#其實這題改為 在正實數可積比較有趣#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#
[問題]高微的問題...
由 cloudsea 於 星期六 二月 25, 2006 4:15 pm
#ed_op#DIV#ed_cl#Prove that f(x) = (sinx)/x is improperly integrable on (0,1) 請問我可以藉著證 f(x) 在趨近於0的極限存在 , 想法是把有問題的點先證它極限存在 , 之後我就不太曉得還需要什麼步驟 ......希望高手可以解惑...謝謝#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#