1. Feb 21, 2012

nesan

1. The problem statement, all variables and given/known data

lim as x -> -1 of the function

(108 (x^2 + 2x)(x + 1)^3) / ((x^3 + 1)^3 (x - 1))

3. The attempt at a solution

Tried in like 10 different ways, came no where close to the answer. I just need someone to point me in the right direction, thank you. :)

2. Feb 21, 2012

SammyS

Staff Emeritus

What were some of the ways you tried?

3. Feb 21, 2012

nesan

Direct substitution gives a 0 / 0.

First, I tried expanding the (x + 1) ^3

to

(x + 1) (x^2 - x + 1)

and (x^3 + 1)^3

to

(x^3 + 1) ((x^3)^2 - x^3 + 1)

That didn't help.

Second, I tried distributing the 108 and everything else on the top into one polynomial, which ended up in a mess.

I'm sure there's an easier way, I just can't seem to figure it out. :(

I tried to find ways to cancel out one term from the bottom, but it always ends up with the opposite sign in the top.

If someone can point me in the right direction, I'll try to get the limit. :)

4. Feb 21, 2012

alanlu

What is the degree of the polynomial in the numerator? What about the denominator?

Last edited: Feb 21, 2012
5. Feb 21, 2012

nesan

I only did the numerator, which has a degree of 5.

I only did the numerator because for some reason I though I could combine all and factor it in a different way, but it ended up in a mess and I lost track of everything. I don't think it is suppose to be this complex.

For example, it has a (x - 1) at the bottom but the closest I can come to matching it is (x + 1) at the top. :(

6. Feb 21, 2012

SammyS

Staff Emeritus

Well, those are incorrect.
(x + 1) (x2 - x + 1) = x3 + 1, not (x+1)3 .

(x + 1)3 = x3 + 3x2 + 3x + 1

Factor the x3+1 in the denominator.
x3+1 = (x+1)(x2 - x + 1)​

Since the x3+1 in the denominator is cubed, that should give a factor in the denominator which cancels with (x+1)3 in the numerator.

7. Feb 21, 2012