# What is the limit of #(3x^2-8x+1)/(2-7x^2)# as x goes to infinity?

##### 1 Answer

#### Explanation:

An attempt to use the quotient rule for limits at infinity gets us the indeterminate form

However,

(when we ask about limits at infinity, we can safely ignore what happens when

The rewritten fraction will have a denominator with a finite limit.

There are at least three ways to describe this rewriting.

1) Divide the numerator and denominator by the greatest power of

2) Multiply numerator and denominator be

3) Factor out the greatest power of

I learned and am still most comfortable with description 3).

# = (cancel(x^2)(3-8/x+1/x^2))/(cancel(x^2)(2/x^2-7))#

# = (3-0+0)/(0-7) = -3/7#

**Remember** the key idea is to rewrite so that the denominator has a finite limit.

**Example 1**

**Example 2**

**Example 3**

find the greatest power of

factor it pout of the numerator and the denominator, and reduce

so the denominator no longer has an infinite limit

the limit of the new denominator is

what is the limit of the new denominator?

If you said

Now what is

If you said

Take a break and have a cookie! Good job.