How Do You Prove the Limit of sin(t)/sqrt(t) as t Approaches Infinity?

[Bipolarity]

Homework Statement

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

Homework Equations

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

 

[kru_]

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

 

[SammyS]

Homework Statement

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

Homework Equations

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

Use the squeeze theorem.

What's $\lim_{t→∞}\ 1/\sqrt{t}\ ?$

How about giving us the entire problem?

 

[micromass]

Are you familiar with the squeeze theorem?

 

[Bipolarity]

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

Thanks guys!

BiP

 

[Bipolarity]

The original problem (for Sammy):

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

BiP