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hanifah

if a>0 what is the lim(x->a) ((sqrt(2xa^3 - x^4)) - a(cuberoot((a^2)(x))))/(a-(ax^3)^(1/4)) What method can help simplify this better? I started by multiplying top and bottom by the conjugate and it was still pretty messy. equation attached in comments for clarity. Any help would be appreciated! thanks

  • 4 months ago
  • 4 months ago

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  1. hanifah
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    • 4 months ago
  2. myininaya
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    Can we use L'hospital's rule?

    • 4 months ago
  3. hanifah
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    Yeah, I tried that first and got a very long/algebraic nightmare.. is it possible to multiply by the conjugate and then us lhr?

    • 4 months ago
  4. myininaya
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    lhospital is working for me

    • 4 months ago
  5. myininaya
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    all you need is one round and then plug in

    • 4 months ago
  6. myininaya
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    remember to treat a as constant

    • 4 months ago
  7. Jonask
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    using L'hospital's rule \[\Large \lim _{x\to a}\frac{\frac{2a^3-4x^3}{2(2ax^3-x^4)^\frac{1}{2}}-a\frac{a^2}{3(a^2x)^\frac {2}{3}}}{-\frac{3ax^2}{4(ax^3)^\frac{3}{4}}}=\frac{-a-\frac{a}{3}}{\frac{-3a^3}{4a^3}}=a\]

    • 4 months ago
  8. hanifah
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    ahhh, so I got the derivatives correct, but I simplified to something that is i don't even know.. haha. honest mistake that will probably kill me on the final=/.. giving the medal to @Jonask this round sorry @myininaya i appreciate the help though!!

    • 4 months ago
  9. myininaya
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    -4/3 divided by -3/4 is 16/9

    • 4 months ago
  10. myininaya
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    Also I didn't give you the answer because I wanted you to do it yourself. lol.

    • 4 months ago
  11. hanifah
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    i know.. @myininaya i'm guessing you're a teacher? haha joking.. jonask doesn't have a medal also I'm not entirely sure what the rules of openstudy are.. i just ask questions, but i feel like some people take the medals pretty seriously. I will sleep on it and get back to you :P

    • 4 months ago
  12. myininaya
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    No I don't care about the medals. I just want the students to be able to get the answers themselves. This isn't suppose to be a site when you can come to cheat.

    • 4 months ago
  13. Jonask
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    yes ...the answer shud be 16a/9...since this was a messy job i decided to write the solution wich u obviously attemted...hence u cud see your mistake

    • 4 months ago
  14. hanifah
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    agree, i couldn't figure out where i messed up via wolfram so open study is the next best thing. i need to improve my algebra

    • 4 months ago
  15. Jonask
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    yes you are write,thats a good idea ,wolfram can help you only if you know ur algebra already,u jus need it for verification and visualisation...we should sharpen ourselves first before we use machines

    • 4 months ago
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