What Happens to sin(1/x) as x Approaches Zero?

[Echo 6 Sierra]

Either I can't find the correct la text or I'm doing it wrong but here goes:

for a limit where x-->0 for sin 1/x

Am I just supposed to recognize that as x goes to zero from the left that it goes to negative infinity and as x goes to zero from the right it goes to positive infinity? What else could I deduce from this?

 

[vincentchan]

the problem is same as
\lim_{x \rightarrow \infty} sin(x)
the limit will oscillate from -1 to 1
(not all limit is define)

 

[Echo 6 Sierra]

Thank you.

 

[Echo 6 Sierra]

For \lim_{x \rightarrow 0} sin \frac{1}{x} could you please explain how it is the same as\lim_{x \rightarrow \infty} sin(x) ? I understand that not all limits can be defined but is it oscillating between -1 and 1 because it can't be defined?

 

[dextercioby]

You need to specify how that limit goes to zero.Either "goes down or up"...

\lim_{x\nearrow 0} or \lim_{x\searrow 0}

Daniel.

 

[vincentchan]

\lim_{x \rightarrow 0^+} sin1/x = \lim_{u \rightarrow {+ \infty}} sin u
\lim_{x \rightarrow 0^-} sin1/x = \lim_{u \rightarrow {- \infty}} sin u

substitude u=1/x and you will see why
sory for the sloppy notation in my first post

 

[HallsofIvy]

However, since none of those limits exist, the distinction is moot.