My Math Forum concerning infinity as the limit involving square roots in the function

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 November 17th, 2017, 10:26 AM #1 Senior Member   Joined: May 2014 From: Allentown PA USA Posts: 111 Thanks: 6 Math Focus: dynamical systen theory concerning infinity as the limit involving square roots in the function Dear MyMathForum Community: In using some notation from the Pascal programming language, As x --> infinity, sqrt(x + 1) / sqrt(4x - 1) = 1/2. Why is this true?
 November 17th, 2017, 10:33 AM #2 Senior Member   Joined: Aug 2012 Posts: 2,356 Thanks: 737 If you square the numerator and denominator, the limit is 1/4. Taking the square root gives you 1/2. Squaring then taking the square root preserves the limit because the square root function is continuous. You'd need to formalize this reasoning to have a homework-ready answer but that's the proof outline. Thanks from topsquark
 November 17th, 2017, 10:45 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 sqrt(4x- 1)= sqrt(4(x- 1/4))= 2sqrt(x- 1/4). As x goes to infinity the "-1/4" is irrelelvant: both sqrt(x) and sqrt(x- 1/4) will go to infinity at the same rate. Thanks from topsquark

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