Show that f(x)=sinxf(x) = \sin xf(x)=sinx is uniformly continuous on R\mathbb{R}R. Which property is key?
∣sinx−siny∣≤∣x−y∣|\sin x - \sin y| \leq |x - y|∣sinx−siny∣≤∣x−y∣ (Lipschitz condition with constant 1)
sinx\sin xsinx is bounded by [−1,1][-1,1][−1,1]
sinx\sin xsinx is periodic with period 2π2\pi2π
sinx\sin xsinx is an odd function