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Typically, it's to give you an idea of a function graphically. Sometimes you deal with functions that are really hectic in design and they don't really have all the points smoothly in place (for example, a graph with an empty point or ^, a peak). A limit gives you an idea of what's happening with the graph as you get close to that point or area (as with infinity not being an actual point), hence the "as x approaches N," N being either some number, or negative or positive infinity.

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Q: Why do we find the limit of a function?
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You need to give more information. Please tell me which trig function and which limit and I will be happy to answer your question. Some of these limits exists and some do not.


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A limit in calculus is a value which a function, f(x), approaches at particular value of x. They can be used to find asymptotes, or boundaries, of a function or to find where a graph is going in ambiguous areas such as asymptotes, discontinuities, or at infinity. There are many different ways to find a limit, all depending on the particular function. If the function exists and is continuous at the value of x, then the corresponding y value, or f (x), is the limit at that value of x. However, if the function does not exist at that value of x, as happens in some trigonometric and rational functions, a number of calculus "tricks" can be applied: such as L'Hopital's Rule or cancelling out a common factor.


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