关于函数一致连续性的几个命题

ON PROPOSITIONS OF UNIFORM CONTINUITY

给出判定函数是否一致连续的几个命题，主要有：若函数ｆ（ｘ）在区间［ａ，＋∞）上连续，且当ｘ→＋∞时，ｆ（ｘ）有渐近线ｙ＝ｋｘ＋ｂ，则ｆ（ｘ）在［ａ，十∞）上一致连续；若函数ｆ（ｘ）是［ａ，＋∞）上单调增加的可导函数，并且其图形在该区间上上凸，则ｆ（ｘ）在［ａ，＋∞）上一致连续；若函数ｆ（ｘ）在区间［ａ，＋∞）上可导，且，则ｆ（ｘ）在［ａ，＋∞）上不一致连续．

A few proposition of uniform continuity are discussed in this article.If f(x) is continuous on [a, +∞) and f(x) has its asymptotic line y=kx+b (asx→+∞, then f(x) is uniformly continuous on[a, +∞). If f(x) is an increasing differentiable function and its figare is convex up on [a, +∞), then f(x) is uniformly Continuous on[a, +∞). If f(x) is a differentiable function on [a, +∞) and lin f' (x)=∞, then f(x) is nat uniformly continuous on[a, +∞).