Piecewise functions are singles collections of sub-functions (each one constituting a “piece”, hence “piecewise”… and why you can think of them as “sub” functions), defined for specific parts of the domain of a graph. When we look at piecewise functions from the perspective of calculus, we’re left with mysteries. Functions are often not differentiable at the intersections of these “sub” functions. With limits, we can gain a better understanding of what’s going on at these intersection points.
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I liked this pencast. However, and I think this goes for all of these pencasts, I think it would help me to see these simple examples along with something more complicated to make me think a little bit more.
This was a good explanation of how to find piecewise function limits. It was very clear and easy to follow. Also, this was a fairly easy example, which makes the concept seem easier than it actually might be. I said this about some of the other pencasts, but I think it would be beneficial if there were a simple example of a topic and then more complicated examples as well.
I agree, this was a fairly easy example of finding piecewise function limits and we could benefit from seeing a harder one also, but I think that could be done by adding another pencast and making it part two (rather than making each pencast longer). This way each person needing the assistance could get as little or as much as they need.