Limits

[bt359]

\(\displaystyle \displaystyle{\lim_{x\, \rightarrow\, 0}\, sinxsin(1/x)}\)


Please help me with above, I dont know how to start. Thank you.

 

[pka]

\(\displaystyle \displaystyle{\lim_{x\, \rightarrow\, 0}\, sinxsin(1/x)}\)
I dont know how to start. Thank you.

Start here
\(\displaystyle 0 \le \left| {\sin (x)\sin ({x^{ - 1}})} \right| = \left| {\sin (x)} \right|\left| {\sin ({x^{ - 1}})} \right| \le \left| {\sin (x)} \right|\)

 

[bt359]

Start here
\(\displaystyle 0 \le \left| {\sin (x)\sin ({x^{ - 1}})} \right| = \left| {\sin (x)} \right|\left| {\sin ({x^{ - 1}})} \right| \le \left| {\sin (x)} \right|\)

Why are we taking the mod? Pls could you finish of your answer I dont get it well.
Thanks.

 

[pka]

Why are we taking the mod? Pls could you finish of your answer .

Well it is your problem. Work on it. We are not here to give out answers.
You asked "where to start?" I answered that.

 

[Deleted member 4993]

Why are we taking the mod? Pls could you finish of your answer I dont get it well.
Thanks.

Because:

sin(x) * sin(1/x) = |sin(x) * sin(1/x)| = |sin(x)| * |sin(1/x)|

 

[bt359]

I still dont get it, anyway... I am just gona ignore this problem, and hope I wont see it later on... its just next level to me.

Thanks Anyway guys... sorry for any trouble.