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 October 11th, 2017, 10:38 AM #1 Senior Member   Joined: May 2014 From: Allentown PA USA Posts: 107 Thanks: 6 Math Focus: dynamical systen theory A proof for a theorem Dear MyMathForum Community: Could someone please furnish me with a proof for the following? when the limit of x --> 0, sin(x)/x = 1. Some of you may recognize this as the "squeeze theorem" or the "pinch theorem." Thank you.
 October 11th, 2017, 11:28 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,767 Thanks: 1422 you've asked this before, haven't you? no matter ... a google search yields a nice hit SqueezeTheorem.pdf Thanks from Carl James Mesaros
 October 12th, 2017, 04:40 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 No, that's not the "squeeze theorem". The "squeeze theorem" involves three functions: If $\displaystyle f(x)\le g(x)\le h(x)$ for all x and $\displaystyle \lim_{x\to a} f(x)= \lim_{x\to a} g(x)= L$ then $\displaystyle \lim_{x\to a} g(x)= L$. Did you mean that you can use the "squeeze theorem" to prove that $\displaystyle \lim_{x\to 0} \frac{sin(x)}{x}= 1$?
 October 12th, 2017, 06:53 AM #4 Senior Member   Joined: May 2014 From: Allentown PA USA Posts: 107 Thanks: 6 Math Focus: dynamical systen theory An apology and a clarification Dear Country Boy, Upon further reading of the proof I desire and the "squeeze theorem", I can say that they are two entirely different concepts. The only thing I want is a proof for: as x --> 0, sin(x)/x = 1. Thank you. Last edited by skipjack; October 12th, 2017 at 08:20 AM.
October 12th, 2017, 07:05 AM   #5
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Quote:
 Originally Posted by Carl James Mesaros The only thing I want is a proof for: as x --> 0, sin(x)/x = 1
Did you check the link in my previous post? A proof of the limit in question is provided as an example of using the squeeze theorem.

October 12th, 2017, 08:50 AM   #6
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Quote:
 Originally Posted by Carl James Mesaros The only thing I want is a proof for: as x --> 0, sin(x)/x = 1. Thank you.
Try looking at the links you've been given in this thread and the last one.

 October 12th, 2017, 10:50 AM #7 Senior Member   Joined: May 2014 From: Allentown PA USA Posts: 107 Thanks: 6 Math Focus: dynamical systen theory Dear Skeeter: I FINALLY got around to the link SqueezeTheorem.pdf. Thanks.
 October 12th, 2017, 11:52 AM #8 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,396 Thanks: 2477 Math Focus: Mainly analysis and algebra A mere three days after you saw the first responses to your first thread asking for the proof. Can you tell me why anybody should bother answering your threads?

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