October 11th, 2017, 11:38 AM  #1 
Senior Member Joined: May 2014 From: Allentown PA USA Posts: 102 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, 12:28 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,679 Thanks: 1339 
you've asked this before, haven't you? no matter ... a google search yields a nice hit SqueezeTheorem.pdf 
October 12th, 2017, 05:40 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,879 Thanks: 766 
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, 07:53 AM  #4 
Senior Member Joined: May 2014 From: Allentown PA USA Posts: 102 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 09:20 AM. 
October 12th, 2017, 08:05 AM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 2,679 Thanks: 1339  
October 12th, 2017, 09:50 AM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,094 Thanks: 2360 Math Focus: Mainly analysis and algebra  
October 12th, 2017, 11:50 AM  #7 
Senior Member Joined: May 2014 From: Allentown PA USA Posts: 102 Thanks: 6 Math Focus: dynamical systen theory 
Dear Skeeter: I FINALLY got around to the link SqueezeTheorem.pdf. Thanks. 
October 12th, 2017, 12:52 PM  #8 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,094 Thanks: 2360 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  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Fermat's last theorem proof  MrAwojobi  Number Theory  20  June 16th, 2014 09:32 PM 
proof by using greens theorem or stokes theorem  george gill  Calculus  5  May 14th, 2011 03:13 PM 
Theorem Proof  HairOnABiscuit  Real Analysis  4  December 17th, 2009 12:37 PM 
Wilson's theorem proof  Ben92  Number Theory  1  July 15th, 2009 12:01 PM 
De l'Hospital's theorem  proof  annakar  Calculus  0  December 31st, 1969 04:00 PM 