Need some help evaluating a limit

  • Thread starter Bipolarity
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  • #1
Bipolarity
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Homework Statement



[tex] \lim_{t→∞}\frac{sin (t)}{\sqrt{t}} [/tex]

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
 

Answers and Replies

  • #2
kru_
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What are the maximum and minimum possible values that sin(t) can ever achieve?
 
  • #3
SammyS
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Homework Statement



[tex] \lim_{t→∞}\frac{sin (t)}{\sqrt{t}} [/tex]

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 [itex] \lim_{t→∞}\ 1/\sqrt{t}\ ?[/itex]

How about giving us the entire problem?
 
  • #4
micromass
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Are you familiar with the squeeze theorem?
 
  • #5
Bipolarity
775
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Ah, good old squeeze theorem why didn't I think of that?

Thanks guys!

BiP
 
  • #6
Bipolarity
775
2
The original problem (for Sammy):

[tex] \int^{π}_{0}\frac{dt}{\sqrt{t}+sin(t)} [/tex]

BiP
 

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