Question

证明sin（1/x）在[1,正无穷)上一致连续

Answer 1

首先,sin(x)在[0,1]连续故一致连续.即对任意ε > 0,存在δ > 0,使x,y ∈ [0,1]满足|x-y| < δ时,总有|sin(x)-sin(y)| < ε.于是对任意a,b ∈ [1,+∞)满足|a-b| < δ,由1/a,1/b ∈(0,1],满足|1/a-1/b| = |a-b|/(ab) ...