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Is this expression infinitesimal, finite, or infinite

  1. Jan 16, 2016 #1
    1. The problem statement, all variables and given/known data
    Say x is an infinitesimal number on the hyperreal line, is this expression finite, infinite or infinitesimal

    2. Relevant equations
    (sqrt(4+x)-2)/x

    3. The attempt at a solution

    My approach so far has been that sqrt(4+x) is (2+y) where y is another infinitesimal and y<x, which seems to lead to the conclusion that this expression is infinite, but the answers say it's finite. Any help?
     
  2. jcsd
  3. Jan 16, 2016 #2

    Samy_A

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    Science Advisor
    Homework Helper

    If ##\sqrt{4+x}=2+y##, where y is infinitesimal, you expression becomes ##\frac{y}{x}##. The quotient of two infinitesimals can be anything: infinitesimal, finite but not infinitesimal, or infinite. Your conclusion is therefore premature (and wrong according to your book).

    What happens when you muliply both numerator and denominator by ##\sqrt{4+x}+2##?
     
    Last edited: Jan 16, 2016
  4. Jan 16, 2016 #3
    ##\frac{1}{\sqrt{4+x}+2}## which is finite. Got it thanks.

    You also taught me how to use the maths notation system on the site. Thanks! (You can see I was a noob before)
     
    Last edited: Jan 16, 2016
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