分类：教育/科学-理工学科-数学
问题：UniformlyContinuousShowthatfunct 
Show that functn f(x)=x^(1/3), the cube root of x, is uniformly continuous on the half closed interval[0,+infinite）
回答：Actually, for an arbrary c>0, there exist n(c) and N(c) >0 such that N(c)> n(c) >0,｜f(x)| < c/2 whenever x < n(c), and｜1/f(x)| < c/2 whenever x > N(c)Moreover, f(x) is uniformly continuous on [n(c)/2,N(c)+n(c)/2], hence there exists an m<n(c)/2 such that|f(x)-f(y)|<c whenever |x-y|<m and x,y in [n(c)/2,N(c)+n(c)/2].Now it is easy to show that we actually have |f(x)-f(y)|<c whenever |x-y|<m and x,y in [0,+infinite)since whenever |x-y|<m, either x,y in [0,n(c)), or [n(c)/2,N(c)+n(c)/2] or or (N(c),+infinite).