Need help trying to do basic limit

  • Thread starter pyrosilver
  • Start date
  • #1
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Homework Statement



lim
[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?

thanks!
 

Answers and Replies

  • #2
jgens
Gold Member
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No need to simplify any further, just note what happens as [itex]h \to 0[/itex]. :wink:
 
  • #3
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Supposedly I can simplify it to

1
----
2[tex]\sqrt{a}[/tex]?
 
  • #4
jgens
Gold Member
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Which is what you get when you evaluate the limit as [itex]h \to 0[/itex].
 
  • #5
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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.
 
  • #6
35,439
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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.

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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