Continuity, epsilin-delta limit definition, uniform continuityThis Demonstration illustrates a theorem of analysis: a function that is continuous on the closed interval [a,b] is uniformly continuous on the interval. A function is continuous if, for each point x0 and each positive number epsilon , there is a positive number delta such that whenever /x-x0/< delta, /f(x) – f(x0)/ < epsilon. A function is uniformly continuous if, for each positive number epsilon, there is a positive number delta such that for all x0, whenever /x-x0/< delta, /f(x) – f(x0)/ < epsilon. In the first case delta depends on both epsilon and x0; in the second, delta depends only on epsilonComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática