[微積分]兩題微積分英文作業

看板trans_math作者 (吻仔魚切片)時間19年前 (2007/01/07 22:37), 編輯推噓1(103)
留言4則, 1人參與, 最新討論串1/1
Suppose that the range of g lies in the domain of f so that the composite f(g(x)) is defined. If f and g are one-to-one, is f(g(x)) also one-to-one? Give reasons for your answer. Is it true that if summation of a[n] for n from 1 to infinity is a divergent series of positive numbers, then there is also a divergent series b[n] for n from 1 to infinity of positive numbers with b[n] < a[n] for every n? Is there a "smallest" divergent series of positive numbers? Give reasons for your answer. 以上兩題.. 該如何解題? 看不太懂... -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.115.213.120

01/08 06:54, , 1F
suppose f(g(x1))=f(g(x2))
01/08 06:54, 1F

01/08 06:55, , 2F
因為f is 1-1,可以implies g(x1)=g(x2)
01/08 06:55, 2F

01/08 06:56, , 3F
又g is 1-1.可以implies x1=x2
01/08 06:56, 3F

01/08 06:57, , 4F
so f(g(x)) is 1-1
01/08 06:57, 4F
文章代碼(AID): #15eGMI5_ (trans_math)