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Find the limit of this function

  1. May 6, 2008 #1
    Hello there

    Find the lim of this function using Algebra alone and without using
    Newton Method or L'Hapital Rule, only Algebraic manipulation is allowed.

    I have previously posted this lim but no one did solve it algebriaclly, I solved it using
    Algebra and uploaded the solution.

    Lim [tex]\frac{^3\sqrt{x}- 4}{\sqrt{x}- 8}[/tex]
    X ---> 64

    The solution
    http://img3.freeimagehosting.net/image.php?ae06b74212.jpg [Broken]
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. May 6, 2008 #2
    Thanks for the update, although I must have missed the original post. It is quite obvious to me that you would want to factor using the difference of two squares/cubes rule as you have 4 (a perfect square) and 8 (a perfect cube). The only thing that might make one hesitate is that instead of using x^2 and x^3 for the numerator and denominator respectively they use x^(1/3) and x(1/2).
  4. May 6, 2008 #3


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    Science Advisor

    That's impressive! Of course, using L'Hopital's rule (which, I notice, you are not allowed to do) would make it fairly simple.
    Last edited by a moderator: May 6, 2008
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