


Limits
For a function f(x),
the limit of the function is the value that the function approaches
as x approaches a certain number. Here’s an example:

Normally, finding the limit should be easy. You would
simply plug the value x approaches, in this case
–2, into the function and produce the limit. But the Math IIC really only
asks one type of question about limits—the test likes to ask you
to determine the limit of a function at a point at which the function
is not defined. But try and plug –2 into the function.
It seems the function is not defined at x =
–2, because division by zero is not allowed. This is precisely what
the test wants you to think. But the assumption
that this function is undefined at –2 is incorrect. And, luckily,
there is an easy way to solve for the limit.
First, you need to factor the function so that it is in
its most simplified state. In our example, the denominator can be
factored:
Once the denominator has been factored, it’s easy to see
that the function ^{x + 2}
/_{(x+2)(x–4)} simplifies
to ^{1}/_{x –
4} . This simplified fraction can be
evaluated at x = –2:
You should choose “the limit does not exist at this point”
answer only if a function is undefinded at the point at which you
wish to find a limit and the function cannot be factored any further.
