Always remember that you can’t divide by zero. Up until now, stumbling upon a situation where you divide by zero leaves you with a mysterious problem that you don’t know how to solve. However, if you understand what limits are, you can figure out what’s going on when you divide by zero. In this problem, I evaluate (think “solve for”) the limit of a function near a hole in it’s graph.
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This is a simple and quick explanation of how to evaluate the limit of a rational function, at a point. This pencast is easy to follow and extremely clear. This example makes it very easy to understand this concept, but a more difficult example in addition to this one would be even better. I think this example does a really good job of explaining how to evaluate the limit of a rational function, at a point in short precise manner.
I found this pencast easy to follow, but I also agree that a more difficult example either in addition to, or instead of the presented one would be very helpful. The basic idea is great to get across, but it's sometimes difficult to apply the basic idea to harder problems. However, the pencast is short, to the point, and easy to follow.