For AP calc students help me please

Ah limits. Essentially, if you have a line or parabola, the limit as x approaches C will be the y value when you plug in x. Unfortunately, it doesn't always work out too nicely. In this example, we need to find f(1-x^2) where x approaches 0. When we plug it in, we learn that we need to find lim f(1). Looking at this graph, f(1) is 2. While this is true, we are not looking for f(1), but rather lim f(1). This means that we are looking for what the y-value gets closer and closer to when x gets closer and closer to 1, but not equal to 1. As you can see, we don't have a nice line to work with. At x=1, we have a few different y-values and no continuous line. In this case, the limit is undefined.

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