## anonymous 4 years ago Show , lim x->0 ( sin 1/x) not equal to 0 use epsilon delta method

1. anonymous

it's lies in the interval -1,1 isn't ?

2. anonymous

nothing like that , prove by epsilon delta , thats all i know ! :p

3. anonymous

LOL!! Nice :))

4. anonymous

LOL ! :p

5. experimentX

http://www.wolframalpha.com/input/?i=lim+x-%3E0+%28+sin+1%2Fx%29 seems like undefined

6. anonymous

is the ans there at this link ?

7. experimentX

it says that limit is undefined

8. anonymous

it's DNE!! :D

9. anonymous

but is it explained ?

10. anonymous

Nopes.

11. anonymous

lol ! I also know the ans , but the prob is explanation ! :p

12. anonymous

This has a somewhat rigorous proof

13. anonymous

This is a simple way to understand: http://mathforum.org/library/drmath/view/53369.html

14. anonymous

really ???

15. anonymous

Yes really!! :D

16. anonymous

thnksss !!!!! :->>

17. anonymous
18. anonymous

Btw nice problem!

19. anonymous

I have many lyk these ! epsilon delta is really gettn on my nerves ! :p

20. anonymous

you are studying single variable or multivariate?

21. anonymous

both ! Actually in eco(h) , maths is subsi ! so its not core maths , but yea its maths , so bound to study ! :p

22. anonymous

lol, great :D :)) I wish I could help you more on epsilon delta proofs my current syllabus only requires to get the answer any how any ways ... so I tend to avoid rigorous stuffs.

23. anonymous

Lucky u ! :>

24. anonymous

lol, I have many many others things to study so not that :P

25. anonymous

Hint if you take the sequence $x_n = \frac{2}{(2n+1)\pi}$ The sequence $x_n$ converges to zero but $\sin\left ( \frac 1{x_n} \right)=\pm 1$