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Homework Help: L'hopitals Derivative

  1. Apr 23, 2008 #1
    [SOLVED] L'hopitals Derivative

    1. The problem statement, all variables and given/known data

    lim x->0 [tex] \frac{1-x^2-e^{-x^2}}{x^4}[/tex]

    I ended up using l'hopitals rule 4 times before I got the answer. And I got an answer of -1/2. I was wondering if someone could check that to see if its right. I would post all my work but that would take a while, however, if you want to see more of my steps ill be glad to do so. I tried graphing it on my calculator, but depending where I put the parenthesis it was right or wrong. Thanks
  2. jcsd
  3. Apr 23, 2008 #2
    My final equation looked like so...

    [tex] \frac{16x^4e^{-x^2} - 24x^2e^{-x^2} + 16x^2e^{-x^2} - 8e^{-x^2} + 8x^2e^{-x^2} - 4e^{-x^2}}{24}[/tex]
  4. Apr 23, 2008 #3
    You can start by replacing x^2 with y in the beginning for nicer equations. I have not been doing anything with l'hopital yet, but I used the infinite series of e^x and got the same answer as you.
  5. Apr 23, 2008 #4
    Ok, I have another question. The derivative of [tex]-e^{-x^2}[/tex] would be [tex]2xe^{-x^2}[/tex] is that correct?
  6. Apr 23, 2008 #5
    i just replaced it with y and that was much easier thanks
  7. Apr 23, 2008 #6


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    yes the derivative is correct as is your solution.
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