I remember the "concept" part of my high school calculus class. The teacher had us recite out loud the epsilon-delta definition of continuity until everybody me

I remember the "concept" part of my high school calculus class. The teacher had us recite out loud the epsilon-delta definition of continuity until everybody memorized it so they could regurgitate it on the test. I always wondered why analogies and pictures weren't used more often: examples: A 100m sprint is a continuous function of time (f(t) = distance from starting line) because sprinters cant teleport. In fact it is uniformly continuous because people have a maximum speed. Beating usain bolt's record is a discontinuous function of completion time because f(world_record + epsilon) = 0 while f(world_record - epsilon) = 1. Fundamental theorem of calculus: If you want to know how fast a guy is running at time t, look at how much ground he covered in 1 second. To get more and more accurate, look at how far he traveled in 0.5 seconds and so on...