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1.不等式e~x≥x+1(x∈R)(1)的几何意义:它表示直线y=x+1是曲线y=e~x在点x=0的切线,且曲线y=e~x在直线y=x+1的上方.2.不等式lnx≤x-1(x>1)(2)的几何意义:它表示直线y=x-1是曲线y=lnx在x=1的切线,且曲线y=lnx在直线y=x-1的下方.这两不等式的作用就是将研究含自然指数
1. The inequality e ~ x≥x + 1 (x∈R) The geometric meaning of (1): It means that the line y = x + 1 is the tangent of the curve y = e ~ x at point x = 0 and the curve y = e ~ x above the straight line y = x + 1. 2. Inequality lnx≤x-1 (x> 1) The geometric meaning of (2): It means the line y = x-1 is the curve y = lnx at x = 1 Tangential, and the curve y = lnx below the line y = x-1.The role of these two inequalities is to study the natural index