Duration: 0:14

A function f(x) is uniformly continous on a interval (a,b) if, for each epsilon greater than zero (blue horizontal ribbon) there is a delta greater than zero, such that | f(x) - f(x+delta) | is less than epsilon for each x in (a,b), which means that the image of the grey vertical ribbon (i.e. the grey horizontal ribbon) falls inside the blue horizontal ribbon. For more information, films, and interactive material, see http://tinyurl.com/4mykly