Need some help evaluating a limit

  • Thread starter Bipolarity
  • Start date
  • #1
775
2

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
85
0
What are the maximum and minimum possible values that sin(t) can ever achieve?
 
  • #3
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,414
1,053

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
22,129
3,298
Are you familiar with the squeeze theorem?
 
  • #5
775
2
Ah, good old squeeze theorem why didn't I think of that?

Thanks guys!

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

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

BiP
 

Related Threads on Need some help evaluating a limit

  • Last Post
Replies
3
Views
560
  • Last Post
Replies
14
Views
1K
  • Last Post
Replies
9
Views
7K
  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
5
Views
8K
  • Last Post
2
Replies
46
Views
4K
Top