Definition of Convergence of Sequence of Functions
Instructions
Use this dynamic activity to explore the definition of convergence of sequence of function using the example of fn(x)=x^n on the interval of [0, 1]. You can also change the f(x) and the interval. Slide n and for each n, find the N such that when nN, fn(x) locates in the -neighborhood.
Reflection Questions
For the sequence of fn(x)=x^n, when n while x is in [0, 1), on the graph what can you conclude about the limit function? How does the limit function change when n while x=1?