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Math - Limits Explained Fast

Math - Limits Explained Fast

Limits are a major concept in mathematics.

Here's an example of using Google to plot a function. In this case I plot the simple function f(x)=1/x

But you can use Google to plot almost any function. It's incredibly helpful.

Anyway, notice there are 4 asymptotes (lines that the function approaches arbitrarily closely but never reaches).

The lines are when:
x-->0 from the plus side and from the negative side.
x-->infinity from the plus side and from the negative side.

The real concept here is very simple, "getting arbitrarily close but never reaching" and mathematics formalizes this idea in the concept of a Limit.

So we say for example, Limit(1/x) as x-->0 is infinity.

But note, and this is critical, in general Limit f(x) as x-->a is not necessarily f(a). So in order to get the limit you CANNOT just substitute x=a in the function. This means that Limits have an independent and important existence.

Content written and posted by Ken Abbott