# What is the limit as x approaches infinity of #ln(x)#?

##### 3 Answers

**To see this, we'll use:**

**and**

**and**

If, on

**We will look at intervals of the form: #[2^n, 2^(n+1)]#**

**On**

And so,

**On**

And,

.

**On each**

And so,

So, as

Since this integral is

The answer is

You can prove it by reductio ad absurdum.

You know that if

You also know that

If

For any strictly increasing function, f, if

Let M be an arbitrary positive number.

Since (as others have shown),

if and only if

Since the numbers themselves increase without bound, we have shown that by making x large enough, we may make

Thus, the limit is infinite as x goes to