Show , lim x-0 ( sin 1/x) not equal to 0
use epsilon delta method

Question

Show , lim x->0 ( sin 1/x) not equal to 0
use epsilon delta method

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

LOL!! Nice :))

anonymous · Answer

LOL ! :p

experimentx · Answer

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

anonymous · Answer

is the ans there at this link ?

experimentx · Answer

it says that limit is undefined

anonymous · Answer

it's DNE!! :D

anonymous · Answer

but is it explained ?

anonymous · Answer

Nopes.

anonymous · Answer

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

anonymous · Answer

This has a somewhat rigorous proof

anonymous · Answer

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

anonymous · Answer

really ???

anonymous · Answer

Yes really!! :D

anonymous · Answer

thnksss !!!!! :->>

anonymous · Answer

http://www.math.washington.edu/~conroy/general/sin1overx/

anonymous · Answer

Btw nice problem!

anonymous · Answer

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

anonymous · Answer

you are studying single variable or multivariate?

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

Lucky u ! :>

anonymous · Answer

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

anonymous · Answer

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