We started exploring limits today in AP Calculus by looking at functions around a point numerically. I wanted to motivate the need for them by giving them a function that had an obvious point where it had a discontinuity, but not an obvious way to simplify it to see if it was a hole or an asymptote. The activity concluded with seven limit problems, for some of which the limit exists, and for some of which it doesn’t – including the infamous sin(1/x) which I am excited to talk about tomorrow.
Students in my non AP Calculus class discovered the power rule today by looking at patterns of derivatives. Some were so excited that they made me give them high fives. Little victories!!!