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anonymous

  • one year ago

Evaluate the limit using L'Hospital's rule if necessary limx→∞ (x^4)e^(−x^2)

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  1. anonymous
    • one year ago
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    \[\lim _{x \rightarrow \infty} x^4e ^{-x^2}\] That's what it looks like :)

  2. anonymous
    • one year ago
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    After simply plugging in 'infinity' for x, I get 'infinity/infinity' which is an indeterminate form and so I can use L'Hopital's Rule

  3. anonymous
    • one year ago
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    I'm not sure if I'm right though...

  4. anonymous
    • one year ago
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    And then I have trouble differentiating this xD

  5. IrishBoy123
    • one year ago
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    you re-wrote it as \(\frac{x^4}{e^{x^2}}\)?

  6. anonymous
    • one year ago
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    Yep! Exactly! Is that right?

  7. IrishBoy123
    • one year ago
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    do differentiate top and bottom...? what do you get?

  8. anonymous
    • one year ago
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    Is it \[\frac{ 4x^3 }{ 2xe ^{x^2} }\] ?

  9. IrishBoy123
    • one year ago
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    and cancel out x's

  10. anonymous
    • one year ago
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    Right! So... \[\frac{ 4x^2 }{ 2e ^{x^2} }\]

  11. anonymous
    • one year ago
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    But then it's still \[\frac{ \infty }{ }\]

  12. anonymous
    • one year ago
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    I mean infinity/ infinity

  13. IrishBoy123
    • one year ago
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    so do L'Hopital again

  14. IrishBoy123
    • one year ago
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    and you can factor the 4/2 as well :p not that it really matters

  15. anonymous
    • one year ago
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    No matter how many times I repeat won't it just keep giving me the same thing?

  16. anonymous
    • one year ago
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    Ahaha true! Kk :D

  17. anonymous
    • one year ago
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    Ohhh actually eventually I get 1/infinity right?!? :O

  18. IrishBoy123
    • one year ago
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    no. keep differentitaing the top and you'll get it down to a constant

  19. IrishBoy123
    • one year ago
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    yes \(e^{x^2}\) is a beast

  20. anonymous
    • one year ago
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    Haha awesomeness! And yeah it sure is a beast XD lol

  21. perl
    • one year ago
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    Correct, you will eventually get \( 1 / \infty \)

  22. anonymous
    • one year ago
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    And that's = 0 :D

  23. anonymous
    • one year ago
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    Ahhh I see! Yeah that makes sense! Thanks so much for the tips! :)

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