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Newbie


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Joined: 23 Jan 2004
Posts: 2247

Posted: 23 Sep 2009 03:42:26 pm    Post subject:

I'm supposed to find a derivative using the limit process of

X
___

X-1


I'm at the stage of

lim
h->0

(X-1)-(X+H-1)
____________________
H(X+H-1)(X-1)


But my weak algebra skills limits me past this.

Am i suppose to multiply this by something to simplify this?
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thornahawk
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Active Member


Joined: 27 Mar 2005
Posts: 569

Posted: 23 Sep 2009 08:42:33 pm    Post subject:

Try simplifying the numerator and canceling common factors; you should be able to arrive at the expected answer. :)

thornahawk
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Newbie


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Joined: 23 Jan 2004
Posts: 2247

Posted: 11 Oct 2009 05:11:45 pm    Post subject:

Another question: I uploaded a picture, 0x5 but it was better than typing all my work. I'm trying to derive 4/sqrt(X) using the limit process but I keep getting -2/X and not the intended answer -2/X^3/2. Can someone look at the picture and tell me where I am going wrong? Thanks.

Edit: BTW thanks for your help thornahawk on the previous problem.


Last edited by Guest on 11 Oct 2009 05:12:50 pm; edited 1 time in total
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Graphmastur


Advanced Member


Joined: 25 Mar 2009
Posts: 360

Posted: 11 Oct 2009 05:46:06 pm    Post subject:

You completely messed up on the ^1/2 part.

(4X^1/2 does not equal 2X. It would equal 2(X^1/2)

And ΔX does not equal X.


Last edited by Guest on 11 Oct 2009 05:47:17 pm; edited 1 time in total
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Newbie


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Joined: 23 Jan 2004
Posts: 2247

Posted: 11 Oct 2009 06:23:12 pm    Post subject:

OK, thanks for clarifying that. What part of my problem would allude you to think that I thought ΔX = X, because I know that's not true. Was it the canceling out or making ΔX = 0 at the end?

Yeah I just realized how bad that error was. I just left everything as 4 and not that weird step I tried to do where I changed it to 2. So in the end I would get -4^(1/2) in the numerator and that would equal -2.

What is it about the denominator that I am doing where I don't get X^(3/2)?

I get X+X^(1/2)ΔX^(1/2) --> X+X^(1/2)(0)^(1/2) = X?


Last edited by Guest on 11 Oct 2009 07:04:03 pm; edited 1 time in total
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thornahawk
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Active Member


Joined: 27 Mar 2005
Posts: 569

Posted: 12 Oct 2009 08:16:18 am    Post subject:

The thing with taking derivatives of radicals via the limit definition is that, contrary to the usual practice of "rationalizing the denominator", you instead "rationalize the numerator".

To be precise, if you bring the whole thing together in the initial expression inside the limit, you should have something like √(x) - √(x+Δx) (or its negative). Multiply the numerator and denominator by √(x) + √(x+h) and simplify from there.

thornahawk
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