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DLS Group Title

Limits question [Challenge]

  • one year ago
  • one year ago

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  1. DLS Group Title
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    \[\LARGE \lim_{x \rightarrow 0} \frac{(1+x)^\frac{1}{x} -e}{x}\]

    • one year ago
  2. DLS Group Title
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    @yrelhan4 @shubhamsrg

    • one year ago
  3. shubhamsrg Group Title
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    * :)

    • one year ago
  4. DLS Group Title
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    first time in life :O

    • one year ago
  5. ParthKohli Group Title
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    Taylor Series expansion?

    • one year ago
  6. DLS Group Title
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    Use whatever you want.

    • one year ago
  7. ParthKohli Group Title
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    Ans 0?

    • one year ago
  8. DLS Group Title
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    Nope

    • one year ago
  9. experimentX Group Title
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    Taylor series works

    • one year ago
  10. ParthKohli Group Title
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    Weird. The Taylor Series expansion is in the terms of \(e\) and \(x\). The first term is \(e\)

    • one year ago
  11. DLS Group Title
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    Taylor series gives 0?

    • one year ago
  12. experimentX Group Title
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    gives -e/2 if you calculate correctly

    • one year ago
  13. ParthKohli Group Title
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    Oh wait! lol, yeah. I forgot to consider that -e/2 which had no \(x\)

    • one year ago
  14. DLS Group Title
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    How about a different way rather than taylor series?

    • one year ago
  15. ParthKohli Group Title
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    Definition of derivative? :-|

    • one year ago
  16. DLS Group Title
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    o.O

    • one year ago
  17. ParthKohli Group Title
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    I was just thinking how this might be the definition of a derivative in disguise.

    • one year ago
  18. experimentX Group Title
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    Binomial expansion might work ... but that's too long

    • one year ago
  19. ParthKohli Group Title
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    DLS Use whatever you want. 15 minutes ago DLS How about a different way rather than taylor series? 9 minutes ago

    • one year ago
  20. DLS Group Title
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    You are right,still investigating for more methods,I wrote so to specify that you are not bound to any particular method,just asking if you know anything alternate :)

    • one year ago
  21. experimentX Group Title
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    L'hopital works

    • one year ago
  22. experimentX Group Title
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    http://www.wolframalpha.com/input/?i=Limit%5B%281+%2B+x%29%5E%281%2Fx%29+%281%2F%28x+%281+%2B+x%29%29+-+Log%5B1+%2B+x%5D%2Fx%5E2%29%2C+x+-%3E+0%5D after using L'hopital you get this expression. The first term tends to e .. if you again apply L'hopital on the second term, you will get -1/2

    • one year ago
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