# Question #21638

##### 2 Answers

When determining the limit of a function, the first thing you should do is replace the variable with the limit itself and see if an answer exists.

In some cases, the denominator becomes 0, indicating a solution does not exist AT the limit. At this point, you proceed with the process of finding the limit (graphing, incremental approach, etc.)

However, in our specific case of:

we actually find that:

VVVVVV incorrect from here, sorry! - Jake VVVVVV

and:

Indicating that:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

A first useful step in solving finite limits is always to try and substitute the value at which you are computing the limit. This can be done for infinite limits too, but infinity is thorny and we can't speak of a mere "substitution" because infinity is not a (real) number and thereby infinity's algebra has to be handled with kid gloves.

If only *continuous functions* are involved (continuous at the point at which you're computing the limit), for finite limits you'll get a finite value. If functions are not all continuous, then there can be some troubles that you have to deal with (indeterminate forms or nonexistence of the limit). For example in case of divisions, when the denominator's limit is

In our case

So this is the case of an indeterminate form

When dealing with

This doesn't restrict its effectiveness in case of

So if

Now the question is: can we work our original limit in some way to get this limit involved? We could multiply the numerator and the denominator by

So by some algebraic manipulations (just properties of fractions) we got

The graph of the function

graph{sin(x^4)/(sin(x^2))^2 [-1.5, 1.5, -1, 2]}