# How do you find the limit #lnx/x# as #x->oo#?

##### 2 Answers

#### Explanation:

If we evaluate the limit of the numerator and denominator separately we'll find that:

Therefore we have a ratio of two infinities

The limit approaches

For example, consider:

We can see that as the denominator gets larger and larger, approaching

#### Explanation:

The question is to find the value of

If we let

So now we can apply L'Hospital's rule by differentiating the numerator and denominator individually.

So,

Now we let

Therefore