• Support PF! Buy your school textbooks, materials and every day products Here!

Help! Prove Lim x-infinity cos(nx) = dne

  • Thread starter bluemax43
  • Start date
  • #1
3
0
Help! Prove Lim x--infinity cos(nx) = dne

Hey guys! I am new here however, I have been lurking around for a while. I need some help with a problem that I am currently working on. Here it is:

Homework Statement



Prove Lim x--infinity cos(nx) = does not exist


The Attempt at a Solution



As of now, I am not quite sure how to approach the problem. I know that I can say that if x is a multiple of 2π then it will converge to 1 however, if it is not a multiple of 2π then it will simply oscillate until infinity. As such, the limit does not exist. However, I doubt that that is what is required of the problem. I am thinking that there must be some systematic setup that I can use to prove this problem otherwise. Is there such a way or is my reasoning correct?

In our other problems, we used epsilon-delta proofs to prove that certain functions converged to p.

Anythings would help! Thanks guys!
 

Answers and Replies

  • #2
26
0


This reminds of a problem I had to do recently. Here are my thoughts:
Pick 2 sequences (x[itex]_{n}[/itex])[itex]_{n}[/itex] and (y[itex]_{n}[/itex])[itex]_{n}[/itex] such that lim x[itex]_{n}[/itex] = infinity as n tends to infinity and lim y[itex]_{n}[/itex] = infinity as n tends to infinity. Then show that lim f(x[itex]_{n}[/itex]) ≠ lim f(y[itex]_{n}[/itex]), therefore the limit does not exist.
 
  • #3
3
0


This reminds of a problem I had to do recently. Here are my thoughts:
Pick 2 sequences (x[itex]_{n}[/itex])[itex]_{n}[/itex] and (y[itex]_{n}[/itex])[itex]_{n}[/itex] such that lim x[itex]_{n}[/itex] = infinity as n tends to infinity and lim y[itex]_{n}[/itex] = infinity as n tends to infinity. Then show that lim f(x[itex]_{n}[/itex]) ≠ lim f(y[itex]_{n}[/itex]), therefore the limit does not exist.
So if I understand your statement correctly, I should choose for example cos(2πn) and show that that the limit goes to 1 and then pick any other to show that it goes to some other number? So basically my reasoning was right?
 
  • #4
26
0


So if I understand your statement correctly, I should choose for example cos(2πn) and show that that the limit goes to 1 and then pick any other to show that it goes to some other number? So basically my reasoning was right?
Yes it is correct.
 
  • #5
3
0


got it thanks!
 

Related Threads on Help! Prove Lim x-infinity cos(nx) = dne

  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
7
Views
1K
Replies
16
Views
6K
Replies
3
Views
905
  • Last Post
Replies
6
Views
4K
  • Last Post
Replies
4
Views
990
  • Last Post
Replies
10
Views
4K
Replies
8
Views
9K
Replies
8
Views
2K
Top