[微積] 數列極限問題2則

[wheniam64 (嘿)]

1. Suppose  that  an →L. Show that if an 小於等於 M for all n,

   then L 小於等於 M .

2. Let f be a function continuous everywhere and let r be a real number.

   Define a sequence as follows:

   a1=r ,  a2=f(r)  ,  a3=f(f(r)) ,  .........

   Prove that if  an→L, then L is a fixed point of f:f(L)=L

這二題習題和同學討論許久不得其解

請版上高手解答

感謝!



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◆ From: 140.112.240.34
→ wheniam64   :an 是數列的第n項  不好意思打不出下標的感覺
推 jacky7987   :f(L)=f(lim_{n->inf}a_n)=lim_{n->inf}f(a_n)
→ jacky7987   :=lim_{n->inf}a_{n+1}=L
→ keroro321   :2.極限定義+連續函數定義想一下就是答案了
推 jacky7987   :1.假設L>M, choose e=(L-M)/2
→ wheniam64   :感謝啊，第二題原來不難XDD