The general expression of a limit is as follows:

Where lim is the abbreviated way of writing limit, x → a is read "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 the study of functions there are points where they have a different or abstract behavior, but at the limit of these points we find things that we do not know how to interpret and we call them **indeterminacies**. Let's see what we can find at the limit of a function:

**0/0 = undetermined**We do not know what result we would obtain if this operation were performed.**(± ∞) / (± ∞) = undetermined**Since we do not know the value of these large numbers, we will not be able to know the exact result.**0 × ∞ = undetermined**We do not know if zero for a number at infinity is some exact value.**∞ - ∞ = undetermined**, we are not sure of the result of these infinite numbers.

Let's see some examples:

**Exercise 1**: Get the value of the following limit

We evaluate the limit at zero:

We find an indeterminacy. To obtain the value of the limit we must find a way to simplify it, in this case, we can make a change of variable, x = √x²:

Once simplified, we reevaluate the limit:

**Exercise 2**: Get the value of the following limit

The first thing we will do is evaluate the limit:

We find an indeterminacy, we must find a way to simplify it; in this case, we can factor the denominator of the summed term:

If we remove the common denominator we have:

Taking common factor 2:

Once the expression has been simplified, we evaluate the limit again: