Need some help evaluating a limit

1. Sep 16, 2012

Bipolarity

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

$$\lim_{t→∞}\frac{sin (t)}{\sqrt{t}}$$

2. Relevant equations

3. The attempt at a solution
This was actually part of a larger problem about improper integrals. The problem has been reduced to this, but I have no idea how to proceed from here. I know that sin(x) behaves very bizarrely at infinity, so I don't know if L'Hopital's rule can even be applied here.

My intuition tells me that the answer is 0, but how can we prove this? Must we refer to the ε-δ definition?

BiP

2. Sep 16, 2012

kru_

What are the maximum and minimum possible values that sin(t) can ever achieve?

3. Sep 16, 2012

SammyS

Staff Emeritus
Use the squeeze theorem.

What's $\lim_{t→∞}\ 1/\sqrt{t}\ ?$

How about giving us the entire problem?

4. Sep 16, 2012

micromass

Are you familiar with the squeeze theorem?

5. Sep 16, 2012

Bipolarity

Ah, good old squeeze theorem why didn't I think of that?

Thanks guys!

BiP

6. Sep 16, 2012

Bipolarity

The original problem (for Sammy):

$$\int^{π}_{0}\frac{dt}{\sqrt{t}+sin(t)}$$

BiP