Limits and continuity
Limits tell us what the limit is as x approaches a constant. There many ways to solve limits algebraically which we will learn in this section. We can also solve limits using L'Hopital's rule. We can plug in x and then find the limit. If the limit is 0/0 that is not the answer. 0/0 is the indeterminate form meaning you haven't found the limit yet. For many function we can see that the following is true.
This means that the limit is continuous. Plugging the constant into the function gives us a constant, that is the limit. Here are some example of continuous limits.
In addition to solving continuous limits, often times we will see limits that aren't solved easily plugging in the constant.
The following example shows us how to solve a limit through factoring.
The following example shows us how to solve a limit through factoring.
Here is an example an when a limit does not exist.
We can also solve limits numerically and graphically.
Graph and create a chart, plugging in numbers around 2, to find the limit.
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The following rules are useful when solving for limits as x approaches infinity.