Prove or disprove (by counterex.)

is unif. cont. on (0,1) and prove or disprove

is unif. cont. on (0,1) for all nonzer0

So I tried getting both into Lipschitz but was not successful. So all I know to do is for the first one is say: Given

set

. If

, then

(it's always going to be < 2 because our interval is (0,1)). Then I say if

and

then

.... How do I know what I should set delta to be? Also I am totally lost starting here. Let me know if these is even remotely on the right track because I don't know for sure. Thank you so much.