I need help finding examples of two types of functions:
1. A continuous function on (0,1) that is not bounded, and
2. A bounded continuous function on (0,1) that is not uniformly continuous
I need help finding examples of two types of functions:
1. A continuous function on (0,1) that is not bounded, and
2. A bounded continuous function on (0,1) that is not uniformly continuous
1) Let f(x) = 1/x on (0,1)
2) Let f(x) = sin(1/x) on (0,1)