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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 homeworkready answer but that's the proof outline.

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.


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function, infinity, involving, limit, roots, square 
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