An Introduction to Limits

Let’s look at a polygon inscribed in a circle. What happens as n gets bigger?

Four true statements: As n gets larger, the n-gon gets closer to being the circle. As n approaches infinity, the n-gon approaches the circle. The limit of the n-gon, as n goes to infinity, is the circle.

Think about the following sequence of numbers: What’s happening to each number? What is the sequence getting closer to? Will it ever reach that value?

So we could write….

What about this one?

Here’s a graph of f(x) =