Limit (mathematics)/Limits

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Limits of Functions



What are limits?


Limits are a way to calculate the value that a function approaches. For instance, we could calculate the value of the function f(x) as x approaches 2. Just as easily we can calculate the value of f(x) as x approaches 20, -2, π, 0, or even ∞.

Why would anyone need limits?


There are a number of reasons that someone might want to use limits:

1. To find the values of functions with asymptotes or missing points
2. To calculate the slope of a point in calculus
3. To prove derivatives in calculus



The notation of a limit function is fairly simple:


This says limit (lim) of f(x) as x approaches p is L.

Usually f(x) is substituted with the contents of the function like so:









Sample Problem Set #1


Let's say we have the function  . If we want to find the limit as x approaches 4, then:


Using two properties of limits:




Our problem becomes:


If we think about the graph of y=b, then we know that the y value never changes. Which means that at any point on that line, we can expect y to be equal to b. So, for any number b:


For us, this means that:


See Also


Wikipedia: Limit of a function