Re: [分析]f>=0且在R上連續且暇積分存在
※ 引述《linshihhua (linshihhua)》之銘言：
: ∞
: 若f is continuous on R and f>=0 and ∫f(x)dx 存在
: -∞
: 請問有辦法證明 lim_(x->∞)f(x)=lim_(x->-∞)f(x)=0嗎?
: 非常感謝幫忙。
the statement is false
here is an counterexample
define f as follows:
f(x)=(x-n)*(2*n^2) if n<x<n+1/(2*n^2)
f(x)=-(x-n-1/n^2)*(2*n^2) n+1/(2*n^2)<=x<n+1/n^2
where n is in N
f(x)=0 otherwise
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