Which of the following functions f:(0,1)→Rf: (0, 1) \to \mathbb{R}f:(0,1)→R is uniformly continuous on (0,1)(0, 1)(0,1)?
f(x)=xsin(1/x)f(x) = x \sin(1/x)f(x)=xsin(1/x)
f(x)=ln(x)f(x) = \ln(x)f(x)=ln(x)
f(x)=1/xf(x) = 1/xf(x)=1/x
f(x)=sin(1/x)f(x) = \sin(1/x)f(x)=sin(1/x)