The Weird Limit Boiz (sinx/x, sin(1/x), & xsin(1/x))

Here is my video submission for BPRP's Brilliant Video Contest! I played around with their Calculus Fundamentals course and the visuals were pretty nice! I took this as an opportunity to talk about the weird limit boiz typically found in a common limits unit in a calc 1 class.

Websites used:
Brilliant
Desmos

Movies referenced at the end:
Sunshine (2007)
Mean Girls (2004)

[EpicMathTime]

The graph of f(x) = sin(1/x) unioned with the point (0, 0) is a very important set called the topologist's sine curve. It is an easy to grasp example of the unintuitive fact that connected sets can fail to be path connected.

If you look at the graph at 5:16, we can see that the graph is surely a connected set. But, there's no path from (0, 0) to any other point in the set (despite the set being fully connected).