[微積分]兩題微積分英文作業
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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