I know that all of the following functions with domain R-{0}, the limit does not exist at 0. However, I'm not sure how to prove them using the Divergence Criterion: f does not have a limit at a if and only if there is an input sequence (xn) with elements in D-{a} such that (xn) converges to a by (f(xn)) diverges.

(1) f(x) = sin(1/x)

(2) f(x) =x+sin(1/x)

(3) f(x)=(1/x)sin(1/x)