Uniform continuity

This video uses animation to contrast the functions f(x) = sin(x) and g(x) = 1/x, visually demonstrating the geometric meaning of "uniform continuity" versus "non-uniform continuity." The sine curve on the left allows finding a uniform δ for any given ε band; whereas the inverse proportional function on the right fails this condition near x=0, where arbitrarily small intervals in x produce large variations in y that exceed fixed ε bands.

Before you watch

• Basic Calculus Limits
• Epsilon-Delta Definition of Continuity