# Boundary evaluation

The general expression of a limit is as follows:

Where lim is the abbreviated way of writing limit, f (x) is the function under study and x → a reads "when x tends to the value a in the function", that is, when the variable x takes values very close to the value a and L is the result of the limit.

In general, when we evaluate a limit we will find indeterminacies or values that we do not know in mathematics, however, thanks to algebra we will be able to "eliminate" these indeterminacies and thus obtain results for them. Let's see some examples:

Exercise 1: Calculate the limit  .

The first thing we will do is replace the value that the x tends to:

We have an indeterminacy, because in mathematics this number has no real meaning; How can we eliminate it?

Factor the limit numerator:

Now if we can evaluate when x = - 1:

So:

Exercise 2: Calculate the limit

The first thing we will do is replace the value that the t tends to:

We have an indeterminacy. We are going to simplify the expression of the limit, we will start with factoring the denominator:

Now we evaluate when t = - 2:

So:

Exercise 3: Calculate the limit .

The first thing we will do is replace the value that the x tends to:

We have an indeterminacy. By simplifying:

Now when evaluating x = 0:

So: