已知函数f﹙x﹚=(1+㏑x)/x (2)如果当x≥2时,不等式f(x)≥a/(x+2)恒成立,求实数a的取值范围
问题描述:
已知函数f﹙x﹚=(1+㏑x)/x (2)如果当x≥2时,不等式f(x)≥a/(x+2)恒成立,求实数a的取值范围
答
f﹙x﹚=(1+㏑x)/x x≥2时,不等式f(x)≥a/(x+2)恒成立(1+㏑x)/x ≥ a/(x+2)a ≤ (x+2)(1+lnx)/x = (1+2/x)(1+lnx) = 1 + 2/x + lnx + 2/x lnx令g(x) = 1 + 2/x + lnx + 2/x lnxg'(x) = -2/x^2 + 1/x - 2/x^2...(2)求证:n≥2,﹙2×3-2﹚﹙3×4-2﹚…[n﹙n+1﹚-2]×[﹙n+1﹚﹙n+2﹚-2]>e^2n-3