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Homework Help: Limit of a function with a radical in numerator

  1. Jan 14, 2014 #1
    1. The problem statement, all variables and given/known data

    Evaluate the limit as x → 0 (zero), if it exists, for:
    [(x+4)^(1/2) - 2]/x

    3. The attempt at a solution

    I was not too sure at an elegant solution because nothing like this existed in the coursework. The best I could think of was to evaluate the limit on each side of zero.

    I tried: evaluate x → 0+ (I used 0.000001)., then I tried: evaluated x → 0- (I used -0.000001). Both of these values are very close to 0.25.

    How can I solve this problem with a little more elegance? Many thanks to the repliers!
    Last edited: Jan 14, 2014
  2. jcsd
  3. Jan 14, 2014 #2


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    Science Advisor

    That function, [tex]\dfrac{\sqrt{x+ 4}- 2}{2}[/tex], is made entirely of continuous functions so is continuous itself. The limit "as x goes to 0" is simply the value at x= 0.
  4. Jan 14, 2014 #3


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    Gold Member

    I don't know if the OP had a typo and fixed it or whether Halls miscopied it but given the expression is$$
    \frac{\sqrt{x+ 4}- 2}{x}$$try rationalizing the numerator.
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