# Squeeze theorem trig question. Please and thanks!

1. Oct 13, 2012

### nukeman

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

Ok, you can see the question and how far I got from the image.

Lim x--> infinity

So, lets take the LEFT side: how does 3x-1 / x turn into just 3?

I know the answer is 3, but from where you can see in the pic, that is where I get stuck, and dont know how to go on from there.

THanks!!!

2. Relevant equations

3. The attempt at a solution

2. Oct 13, 2012

### tiny-tim

hi nukeman!
the 1 becomes insignificant compared to 3x as x -> ∞, so that leaves you with 3x/x, which is 3

alternatively: (3x-1)/x = 3 - 1/x, and 1/x -> 0 as x -> ∞, so 3 - 1/x -> 3

3. Oct 13, 2012

### nukeman

How does the 1 become insignificant? That is what I am having trouble understanding. :(

4. Oct 13, 2012

### tiny-tim

because the 3x becomes 30000 then 30000000000 then 300000000000000 and so on, and the tiddly little 1 doesn't matter much any more

5. Oct 13, 2012

### SammyS

Staff Emeritus
It generally helps us, if you state the problem you're trying to solve.

In this case it appears to be:
Find $\displaystyle \lim_{x\,\to\,\infty} \frac{3x+\cos^2(100x)}{x}\ .$​

By the way: $0\le \cos^2(100x)\le 1\ .$

6. Oct 13, 2012

### nukeman

why is it 0≤ instead of -1?

7. Oct 13, 2012

### SammyS

Staff Emeritus
I meant to ask you !

8. Oct 13, 2012

### nukeman

limit as x -> infinity of [ 3x + cos^{2}(100x)] / x

I thought it would -1 ≤ cos^2(100x) ≤ 1

since a cos has amplitude of -1 and 1 ?

9. Oct 14, 2012

### SammyS

Staff Emeritus
Right regarding cos(x).

How about cos2(x)? Is that ever negative?

10. Oct 14, 2012

### nukeman

wow, how did I NOT know that! :(

Ok thanks... I got that now.

So the left side would be 3x/x correct? so, then I would put each term over x, leaving 3 and 1 (3 * 1 = 3) correct?

11. Oct 14, 2012

### SammyS

Staff Emeritus
Please write the expression that you're trying to describe .