Homework Help: 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 .