Question

(2x^2+1)/[(x-1)^2(x^2+x)] as the limit approaches infinity

Answer 1

Ok, so first we want to find where the greater power is - because like, if the bottom has a greater power, it will increase faster than the top, and the equation will go to zero since the bottom is so large, right? :)

Answer 2

yes, thats right. So that means I have to drop the (x^2+x) in the bottom?

Answer 3

So first, let's try simplifying the bottom, right?
We know we're going to get at least one x^2 from (x-1)^2, and if we multiply this by another X^2, we should get X^4, right?

Answer 4

Oh, no, just pay attention to the x values to see if they will become larger than those on the top. Does that make sense thusfar?

Answer 5

oh wait. I made a mistake with the top part. Its (2x^2+1)^2

Answer 6

Ok, so let's simplify the top and bottom.

Answer 7

Sorry! and yes it makes sense :)

Answer 8

We're going to get 4X^4 as one of the answers on the top, right?

Answer 9

and since we know we're getting x^4 on the bottom, we're in a sort of dilemma - normally one expands faster than the other, but these have the same powers. But the thing is, the top is 4 while the denominator is 1.
The idea is that the limit then goes to 4, which is the coefficent of these numbers - the infinities below will cancel out since they increase the same amount, and we will have 4 as our answer.

Answer 10

I can explain that more since it is kind of confusing, if you'd like

Answer 11

I was working out the problem. I understand where I made the mistake I was supposed to distribute. I used the chain rule instead which made the problem much more confusing.

Answer 12

Thank you very much for your help

Answer 13

Ok, cool! :) Yeah, with limits that go to infinity, just look at the leading powers.