# How do you find the limit of #sqrt(x-3)/(x-9)# as x approaches 9?

##### 2 Answers

#### Explanation:

Let's try direct substitution.

So there is a "hole" at

The answer you are expected to write depends, in part, on where and with whom you are studying Calculus.

#### Explanation:

In James Stewart's *Calculus* (used at many college and universities in the US), the final answer to this question is "Does Not Exist".

As **through positive values**.

As

We write:

Coming from the left, we still get the numerator approaching a positive limit, by now, as **through negative values**.

As

We write:

In this case, our Stewart (and others) adopt the convention that the limit (that is, the "two-sided" limit) simply does not exist.

We write:

Of course, "infinite limits" do not exist either, but when we write, for example: **why** the limit does not exist. (Because the quotient increases without bound.)