Thread: 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!

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.