# use squeeze theorem to

• Jun 7th 2012, 06:50 AM
sluggerbroth
use squeeze theorem to
use squeeze theorem to establish limit

lim (as x goes to zero) of x sin(1/x)=0

also help with keying problem? symbosl etc?
• Jun 7th 2012, 06:59 AM
Krahl
Re: use squeeze theorem to
For all $\displaystyle x \in \Re$,
$\displaystyle -1 \leq sin(x) \leq 1$.

This is also valid for $\displaystyle 1/x \in \Re$ $\displaystyle x \neq 0$,
$\displaystyle -1 \leq sin(1/x) \leq 1$.

Multiply by $\displaystyle x$ and apply the squeeze theorem.

Examples of using Latex (the symbols) can be found here http://mathhelpforum.com/latex-help/...ags-latex.html and http://mathhelpforum.com/latex-help/...-tutorial.html
• Jun 7th 2012, 07:06 AM
Reckoner
Re: use squeeze theorem to
Quote:

Originally Posted by Krahl
For all $\displaystyle x \in \Re$,
$\displaystyle 0 \leq sin(x) \leq 1$.

I think you mean, for all $\displaystyle x$, $\displaystyle -1\leq\sin x\leq1$.
• Jun 7th 2012, 07:07 AM
Plato
Re: use squeeze theorem to
Quote:

Originally Posted by sluggerbroth
use squeeze theorem to establish limit
lim (as x goes to zero) of x sin(1/x)=0
also help with keying problem? symbosl etc?

Learn LaTeX coding.
[TEX]{\lim _{x \to 0}}x\sin \left( {\frac{1}{x}} \right)[/TEX] gives $\displaystyle {\lim _{x \to 0}}x\sin \left( {\frac{1}{x}} \right)$.
• Jun 7th 2012, 07:17 AM
Krahl
Re: use squeeze theorem to
Quote:

Originally Posted by Reckoner
I think you mean, for all $\displaystyle x$, $\displaystyle -1\leq\sin x\leq1$.

Sorry, yes that's the one.