作者j95300 (吻仔魚切片)
看板trans_math
標題兩題微積分英文作業
時間Sun Jan 7 22:37:05 2007
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.
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◆ From: 140.115.213.120
1F：推 vu3cj0su3:suppose f(g(x1))=f(g(x2)) 218.160.159.81 01/08 06:54
2F：→ vu3cj0su3:因為f is 1-1,可以implies g(x1)=g(x2) 218.160.159.81 01/08 06:55
3F：→ vu3cj0su3:又g is 1-1.可以implies x1=x2 218.160.159.81 01/08 06:56
4F：→ vu3cj0su3:so f(g(x)) is 1-1 218.160.159.81 01/08 06:57