Limit problem that stumped me

Might be overlooking something simple, but I'm having trouble figuring this out:

As x approaches infinity, what is the limit of

( -5x^7 + 5x^6 - 3x^5 - 4x^4 ) / ( -7x^4 + x^3 )

I narrowed it down to this:

( -5x^3 + 5x^2 - 3x - 4 ) / -7

Then plugged-in infinity where x is...

( -∞ + ∞ - ∞ - 4 ) / -7

Then I don't know what to do because I can't subtract infinity from infinity...

Someone please explain in detail how to solve this and other problems like it. Thanks in advance!

Re: Limit problem that stumped me

Quote:

Originally Posted by

**TWN** Might be overlooking something simple, but I'm having trouble figuring this out:

As x approaches infinity, what is the limit of

( -5x^7 + 5x^6 - 3x^5 - 4x^4 ) / ( -7x^4 + x^3 )

I narrowed it down to this:

( -5x^3 + 5x^2 - 3x - 4 ) / -7

Then plugged-in infinity where x is...

( -∞ + ∞ - ∞ - 4 ) / -7

Then I don't know what to do because I can't subtract infinity from infinity...

Someone please explain in detail how to solve this and other problems like it. Thanks in advance!

degree numerator > degree of the denominator, the rational function will either increase or decrease w/o bound.

if you did not learn all this in precalculus (and you should have), then check this out ...

Rational Functions

... scroll down to **Rational function end behaviors are all about ratios**, but I recommend you look over the entire article.