My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

Thanks Tree2Thanks
  • 1 Post By Maschke
  • 1 Post By Country Boy
LinkBack Thread Tools Display Modes
November 17th, 2017, 11:26 AM   #1
Senior Member
Joined: May 2014
From: Allentown PA USA

Posts: 102
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?
Carl James Mesaros is offline  
November 17th, 2017, 11:33 AM   #2
Senior Member
Joined: Aug 2012

Posts: 1,661
Thanks: 427

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
Maschke is offline  
November 17th, 2017, 11:45 AM   #3
Math Team
Joined: Jan 2015
From: Alabama

Posts: 2,875
Thanks: 766

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
Country Boy is offline  

  My Math Forum > College Math Forum > Calculus

function, infinity, involving, limit, roots, square

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
limit with square roots Melody2 Calculus 25 November 2nd, 2013 07:32 AM
System of equations involving square roots fantom.1040 Algebra 2 July 2nd, 2011 07:04 AM
help with infinity limit with square roots denethor101 Calculus 2 September 6th, 2009 06:57 PM
Limit of a function as it approaches infinity vthokie11 Calculus 1 February 10th, 2009 06:04 PM
limit with square roots Melody2 Elementary Math 6 December 31st, 1969 04:00 PM

Copyright © 2017 My Math Forum. All rights reserved.