# How do you find the Limit of # (2x+3)[ln(x^2-x+1)-ln(x^2+x+1)]# as x approaches infinity?

##### 1 Answer

Please see below.

#### Explanation:

The initial form is

Rewriting

lets us see that, since

So rewrite the original expression as

The initial form of this limit is

It takes some algebra for the numerator, but the quotient of the derivatives is

The limit, as

**One way** to see this is to expand (or describe the expansion of) the polynomials.

We'll get

Dividing numerator and denominator by

So the limit is

**Another way**, a bit more explicit

The limit at infinity is