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Homework Help: Need help trying to do basic limit

  1. Nov 9, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]_{}h\rightarrow0[/tex] ([tex]\sqrt{a+h}[/tex] - [tex]\sqrt{a}[/tex]) / h

    3. ok so i multiplied by [tex]\sqrt{a+h}[/tex] + [tex]\sqrt{a}[/tex]. The top simplified to a+ h -a, aka h. the bottom is h([tex]\sqrt{a+h}[/tex] + [tex]\sqrt{a}[/tex]).

    The h cancels, so I am left with

    1 / ([tex]\sqrt{a+h}[/tex] + [tex]\sqrt{a}[/tex]

    how do i simplify this further?

  2. jcsd
  3. Nov 9, 2009 #2


    User Avatar
    Gold Member

    No need to simplify any further, just note what happens as [itex]h \to 0[/itex]. :wink:
  4. Nov 9, 2009 #3
    Supposedly I can simplify it to

  5. Nov 9, 2009 #4


    User Avatar
    Gold Member

    Which is what you get when you evaluate the limit as [itex]h \to 0[/itex].
  6. Nov 10, 2009 #5
    It makes perfect sense as well that that is your answer. I am not sure of the extent of your understanding of differentiation, however, if you know enough, you should be able to recall that the derivative of a^(1/2) = 1/2a^(1/2) which is exactly what you got.
  7. Nov 10, 2009 #6


    Staff: Mentor

    A clearer way of writing this would be a^(1/2) = 1/(2a^(1/2)). A literal reading of what you wrote would be 1/2*a^(1/2); that is, the fractional power would be in the numerator, which I'm sure you didn't intend.
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