已知函数f(x)=(1+㏑x)/x,(x≥1) (1)试判断函数f(x)的单调性,并说明理由(2)若f(x)≥k/x+1恒成立,求实数k的取值范围(3)求证:[(n+1)!]²>(n+1)e(n-2)(这里为e的n-2次
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![已知函数f(x)=(1+㏑x)/x,(x≥1) (1)试判断函数f(x)的单调性,并说明理由(2)若f(x)≥k/x+1恒成立,求实数k的取值范围(3)求证:[(n+1)!]²>(n+1)e(n-2)(这里为e的n-2次](/uploads/image/z/3976881-33-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D%EF%BC%881%2B%E3%8F%91x%EF%BC%89%EF%BC%8Fx%2C%EF%BC%88x%E2%89%A51%EF%BC%89+%EF%BC%881%EF%BC%89%E8%AF%95%E5%88%A4%E6%96%AD%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%8D%95%E8%B0%83%E6%80%A7%2C%E5%B9%B6%E8%AF%B4%E6%98%8E%E7%90%86%E7%94%B1%EF%BC%882%EF%BC%89%E8%8B%A5f%EF%BC%88x%EF%BC%89%E2%89%A5k%EF%BC%8Fx%2B1%E6%81%92%E6%88%90%E7%AB%8B%2C%E6%B1%82%E5%AE%9E%E6%95%B0k%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%EF%BC%883%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9A%5B%EF%BC%88n%2B1%EF%BC%89%21%5D%26%23178%3B%EF%BC%9E%EF%BC%88n%2B1%EF%BC%89e%EF%BC%88n-2%EF%BC%89%EF%BC%88%E8%BF%99%E9%87%8C%E4%B8%BAe%E7%9A%84n-2%E6%AC%A1)
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