Section 1.2  Limits, a Formal Definition
Our informal definition was based on some very loose language like "close to". In this lecture, we're going to make that more precise. From a high level, the idea is that if there's a point, y, close to the limit on the yaxis then there has to be a corresponding point close to the limit value on the xaxis that the function maps to that point. This is illustrated in the exploration below.
The function on the graph is $f(x) = 1.25x  .5$ and we're looking at $\lim\limits_{x\to 1} f(x)$. I'm going to claim that the limit is equal to $f(1) = .75$. The directions below will walk you through our new definition of "close to".

