因为lim(x→正无穷)f(x)存在,
所以存在X>0,M>0
使得,当|x|>X时,
|f(x)|≤M
又在区间【-X,X】上函数是连续的,根据闭区间函数连续的定理
可知,f(x)在【-X,X】上有界,从而
f(x)在R内有界
证明:若f(x)R内连续,且lim(x→正无穷)f(x)存在,则f(x)在R内有界
证明:若f(x)R内连续,且lim(x→正无穷)f(x)存在,则f(x)在R内有界
数学人气:797 ℃时间:2019-09-13 19:24:53
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