常见不等式及其关系(1)xx22把x换成把x换成33x23xe≥ex>x2(x>0)xe≥ex>1x34e≥ex2722xex≥x+lnx+1ex>x4把x换成x-1把x换成x把x换成x+lnx2x把x换成-x3把x换成丢掉常数项1取倒数xx3-xx1e>xxe≤(x<1)27e>xe≥x+1e≥-x+11-x把x换成-x把x换成x-1,x-ln2等2取倒数x1把换把x换-xxxexe<-(x<0)e>-xxe≥ex+,e≥2x+2-2ln2x成e成lnx2xlnx≥x-1把x换成x丢掉常数项-1把x换成1xlnx≥1-1lnx<2xlnx0)x把x换成ex,x等把x换成1e把x换成x2xlnx≤ex-2,lnx≤xelnx>-1lnx>-12x2xln(1+x)≤x(x>-1)1*1*取x=n∈ℕ取x=-n∈ℕnn+11>ln(n+1)-lnn1e2<x1-x2x1-x22x1x2x1x2把x1,x2换成e,e把x1,x2换成e,ex1-x2x1-x2x1+x2>x1x21),lnx>x-1(0(x-)2(x-1)2(x-1)2x2xlnx>x+1lnx1)(01)(02x(x>0)ln(1+x)<2x(-1ln(1+n)ln(1+)>352n+1n2n+1第2页共2页第2/2页