## anjali_pant 3 years ago Show , lim x->0 ( sin 1/x) not equal to 0 use epsilon delta method

1. FoolForMath

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

2. anjali_pant

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

3. FoolForMath

LOL!! Nice :))

4. anjali_pant

LOL ! :p

5. experimentX

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

6. anjali_pant

is the ans there at this link ?

7. experimentX

it says that limit is undefined

8. FoolForMath

it's DNE!! :D

9. anjali_pant

but is it explained ?

10. FoolForMath

Nopes.

11. anjali_pant

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

12. FoolForMath

This has a somewhat rigorous proof

13. FoolForMath

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

14. anjali_pant

really ???

15. FoolForMath

Yes really!! :D

16. anjali_pant

thnksss !!!!! :->>

17. FoolForMath
18. FoolForMath

Btw nice problem!

19. anjali_pant

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

20. FoolForMath

you are studying single variable or multivariate?

21. anjali_pant

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

22. FoolForMath

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. anjali_pant

Lucky u ! :>

24. FoolForMath

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

25. eliassaab

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