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DLS

  • 2 years ago

Limits question [Challenge]

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  1. DLS
    • 2 years ago
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    \[\LARGE \lim_{x \rightarrow 0} \frac{(1+x)^\frac{1}{x} -e}{x}\]

  2. DLS
    • 2 years ago
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    @yrelhan4 @shubhamsrg

  3. shubhamsrg
    • 2 years ago
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    * :)

  4. DLS
    • 2 years ago
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    first time in life :O

  5. ParthKohli
    • 2 years ago
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    Taylor Series expansion?

  6. DLS
    • 2 years ago
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    Use whatever you want.

  7. ParthKohli
    • 2 years ago
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    Ans 0?

  8. DLS
    • 2 years ago
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    Nope

  9. experimentX
    • 2 years ago
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    Taylor series works

  10. ParthKohli
    • 2 years ago
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    Weird. The Taylor Series expansion is in the terms of \(e\) and \(x\). The first term is \(e\)

  11. DLS
    • 2 years ago
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    Taylor series gives 0?

  12. experimentX
    • 2 years ago
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    gives -e/2 if you calculate correctly

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

  14. DLS
    • 2 years ago
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    How about a different way rather than taylor series?

  15. ParthKohli
    • 2 years ago
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    Definition of derivative? :-|

  16. DLS
    • 2 years ago
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    o.O

  17. ParthKohli
    • 2 years ago
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    I was just thinking how this might be the definition of a derivative in disguise.

  18. experimentX
    • 2 years ago
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    Binomial expansion might work ... but that's too long

  19. ParthKohli
    • 2 years ago
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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

  20. DLS
    • 2 years ago
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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 :)

  21. experimentX
    • 2 years ago
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    L'hopital works

  22. experimentX
    • 2 years ago
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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

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