Talk:Limit of Sine of X over X

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There's another way to prove it if someone more adept than me would like to tackle it. In involves first proving that for all x in the open interval (pi/2, pi/2)

|1/2 sin(x)| < |1/2 x| < |1/2 tan(x)|

$\implies$ |sin(x)/sin(x)| < |x/sin(x)| < |tan(x)/sin(x)|

$\implies$ |1| < |x/sin(x)| < |1/cos(x)|

$\implies$ 1 > sin(x)/x > cos(x)

And then using the squeeze theorem. I don't know how to write the proof in a way that's wiki-worthy. - Joshua Haber, September 22, 2011

Writing in $\LaTeX$ is easy to learn, and it is a good skill for a mathematician to have. There are plenty of examples on this site to follow. --prime mover 00:32, 22 September 2011 (CDT)

Yeah but I don't know how to make computer pictures of geometric objects. If someone can make them for me I guess I can give it a shot. I need the following diagrams

1) a triangle ABC with the following properties

A = (0,0), B = (1,0), C is a point on the unit circle in quadrant I. $\angle{CAB}$ needs a little $\theta$ in it.

2) a circular sector subtended by arc BC with vertex A. $\triangle$ABC inscribed in it

C) A triangle ABD where A, C, and D are collinear and $\overline{AB} \perp \overline{BD}$. The circular sector in inscribed in it and $\triangle$ABC is further inscribed in that.

Is there a way I can make computerized drawings of these online? - Joshua Haber, September 23, 2011

I use the Geogebra package. Recommended. --prime mover 14:56, 22 September 2011 (CDT)


Working on it here now that I got the basics of $\LaTeX$--GFauxPas 14:13, 25 September 2011 (CDT)


Yes, we can tidy it up. As for making it look more pretty, the house style is as it is. I think it looks fine. Once it's been arranged neatly we can see what it looks like. This will be done in due course. --prime mover 16:59, 25 September 2011 (CDT)
If we are going to cite the Mathworld source, can you point me towards the exact page? --prime mover 03:16, 26 September 2011 (CDT)
... the proof has been put into its own subpage (which is what we do when there are multiple proofs and they're long): Limit of Sine of X over X/Geometric Proof.
I have tidied it and put it into house style, and "depersonalised" some of the language.
Good job. --prime mover 04:34, 26 September 2011 (CDT)

Thanks very much prime.mover, I knew "squeeze as hard as you can and don't let go" was a bit non-rigorous and I'm glad someone put me in my place :) The main source was this video

http://www.khanacademy.org/video/proof--lim--sin-x--x?playlist=Calculus

The secondary source was this book :

Calculus, Eigth Edition, by Larson, Hostetler, and Edwards

The wolfram mathworld site I used was

http://mathworld.wolfram.com/CircularSector.html

I appreciate you giving me the excuse to learn a bit a $\LaTeX$ prime mover and maybe I'll do a few more proof when I feel like it. --GFauxPas 07:03, 26 September 2011 (CDT)

Got the sources. As for the Wolfram page, it's relevant to one tiny part of the proof which has been extracted into a separate page anyway, so I'll move it into there. --prime mover 07:17, 26 September 2011 (CDT)

Prime.mover, can/should should I add a little sub-page for the corollary lim x->0 x/sin(x) = 1 ? I don't know if it's significant enough to be considered a corollary and not a lemma.--GFauxPas 07:31, 26 September 2011 (CDT)

If you like. I've added the corollary, you add the proof. --prime mover 08:15, 26 September 2011 (CDT)