设函数f(x)在区间[a,+∞)上连续,有lim(x→+∞)f(x)存在且有限.证明:f(x)在[a,+∞)上有界
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![设函数f(x)在区间[a,+∞)上连续,有lim(x→+∞)f(x)存在且有限.证明:f(x)在[a,+∞)上有界](/uploads/image/z/2623943-47-3.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%E5%8C%BA%E9%97%B4%5Ba%2C%2B%E2%88%9E%EF%BC%89%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E6%9C%89lim%28x%E2%86%92%2B%E2%88%9E%29f%28x%29%E5%AD%98%E5%9C%A8%E4%B8%94%E6%9C%89%E9%99%90.%E8%AF%81%E6%98%8E%EF%BC%9Af%EF%BC%88x%EF%BC%89%E5%9C%A8%5Ba%2C%2B%E2%88%9E%EF%BC%89%E4%B8%8A%E6%9C%89%E7%95%8C)
设函数f(x)在区间[a,+∞)上连续,有lim(x→+∞)f(x)存在且有限.证明:f(x)在[a,+∞)上有界
设函数f(x)在区间[a,+∞)上连续,有lim(x→+∞)f(x)存在且有限.证明:f(x)在[a,+∞)上有界
设函数f(x)在区间[a,+∞)上连续,有lim(x→+∞)f(x)存在且有限.证明:f(x)在[a,+∞)上有界
因为lim(x→+∞)f(x)存在且有限,设为C
根据定义,任意ε>0,存在X>a,当x>X,有|f(x)-C|