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November 17th, 2017, 10:26 AM   #1
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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?
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November 17th, 2017, 10:33 AM   #2
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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.
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November 17th, 2017, 10:45 AM   #3
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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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