Thread: Limits Help

Hi there,
just pondering this equation: lim (3x^3(-6x^2)+5x+35)/((x^4)-5x^3-27) when x->∞

what is the best way to figure this out? I tried to divide everything by the highest factor I would find in the denominator, like my textbook said, but that just got messy and confusing. Any ideas?

Is the limit actually:

?

If so, you might just observe that the limit is zero since the degree in the denominator is greater than that of the numerator.

oh, ok then, that means that I did get it right (I came out with 0/1), but what confused me was that wolfram indicated it was -infinity. Glad I seem to have done the right thing then!!

I don't see how you could have gotten . The reason the limit is is because the denominator goes to while the numerator does not. Dividing a number by a much larger number gives you something very close to 0.

If you typed it into the text box at wolfram as you did in your first post, then you would get -infinity. Do you see why?

ahh, it was all those unnecessary brackets I put in... silly me

in that particular wolfram working, it divides each term by a different power... why is this? I thought we would only divide by x^4??

They DID divide top and bottom by ...

so what about where they divided by x^3, x^2?? Sorry i know I sound like a complete idiot, but these things take time to sink in

Oh, now I get it!! Thank you so much!

Originally Posted by NettieL

Oh, now I get it!! Thank you so much!

Also a good thing to remember when solving limits that tend to infinity is that you can take the highest power in the numerator over the highest power in the denominator and calculate the limit of that. In your case it would be 3x^3/x^4 which would simplify to 3/x and the limit of 3/x as x tends to -infinity is obviously 0.