Expert: Paul Klarreich - 3/14/2011

Question
What is the limit as x tends to infinity of x/(sqr(4x^2-x+3)) and show how

Answer
Questioner: Anne
Country: New Zealand
Category: Calculus
Private: No
Subject: Limits
Question: What is the limit as x tends to infinity of x/(sqr(4x^2-x+3)) and show how
..............................
      x
-----------------
sqrt(4x^2 - x + 3)

Try this trick:
Divide top and bottom by x:

      x / x
-----------------------
sqrt( 4x^2 - x + 3) / x

      x / x
------------------
sqrt(( 4x^2 - x + 3) / x^2 )  << under the radical,  x becomes x^2


         1
-------------------------------
sqrt( 4x^2/x^2 - x/x^2 + 3/x^2)


         1
------------------------
sqrt( 4 - 1/x + 3/x^2)

I think you can finish up.