My Math Forum A proof for a theorem

 Calculus Calculus Math Forum

 October 11th, 2017, 10:38 AM #1 Member   Joined: May 2014 From: Allentown PA USA Posts: 97 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: 2,639 Thanks: 1319 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: 2,719 Thanks: 699 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 Member   Joined: May 2014 From: Allentown PA USA Posts: 97 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
Math Team

Joined: Jul 2011
From: Texas

Posts: 2,639
Thanks: 1319

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
Math Team

Joined: Dec 2013
From: Colombia

Posts: 6,970
Thanks: 2290

Math Focus: Mainly analysis and algebra
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 Member   Joined: May 2014 From: Allentown PA USA Posts: 97 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: 6,970 Thanks: 2290 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?

 Tags proof, theorem

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post MrAwojobi Number Theory 20 June 16th, 2014 08:32 PM george gill Calculus 5 May 14th, 2011 02:13 PM HairOnABiscuit Real Analysis 4 December 17th, 2009 11:37 AM Ben92 Number Theory 1 July 15th, 2009 11:01 AM annakar Calculus 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top