设f(x)在[0,∞)上连续,且当x>0时,0

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设f(x)在[0,∞)上连续,且当x>0时,0

设f(x)在[0,∞)上连续,且当x>0时,0
设f(x)在[0,∞)上连续,且当x>0时,0

设f(x)在[0,∞)上连续,且当x>0时,0
只需证明:f(x)递增有上界:
事实上,
1)f(x)递增有导数大于0得到;
2)f(x)有上界:
利用f(x)=f'(s)从1积分到x,再加上f(1).
因为f'(x)