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El_Arrow

  • one year ago

need help finding the limit

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  1. El_Arrow
    • one year ago
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    \[\lim_{n \rightarrow \infty} \frac{ 1 }{ n*3^n }\]

  2. freckles
    • one year ago
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    you can say what is happening to the bottom there as n gets big?

  3. Astrophysics
    • one year ago
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    Let it be \[\frac{ \lim_{n \rightarrow \infty} 1 }{ \lim_{n \rightarrow \infty} n3^n}\]

  4. El_Arrow
    • one year ago
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    its getting closer to 0?

  5. freckles
    • one year ago
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    are you saying that about the whole fraction?

  6. El_Arrow
    • one year ago
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    no just the bottom

  7. Astrophysics
    • one year ago
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    Noppppe

  8. El_Arrow
    • one year ago
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    the whole fraction?

  9. Astrophysics
    • one year ago
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    I mean if we look at the denominator as freckles is telling you, would you really think it's approaching 0?

  10. El_Arrow
    • one year ago
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    i would think

  11. Astrophysics
    • one year ago
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    You can split it even further as follow \[\lim_{n \rightarrow \infty} n \lim_{n \rightarrow \infty} 3^n\] still think it's approaching 0?

  12. freckles
    • one year ago
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    \[5 \cdot 3^5 \text{ big number } \\ 100 \cdot 3^{100} \text{ Even bigger number } \\ 1000 \cdot 3^{1000} \text{ much much more bigger }\]

  13. El_Arrow
    • one year ago
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    yeah its definitely going to infinity

  14. Astrophysics
    • one year ago
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    yeah haha, so what will the whole thing be?

  15. Astrophysics
    • one year ago
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    Note the numerator is 1!!

  16. El_Arrow
    • one year ago
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    1/infinty=0

  17. Astrophysics
    • one year ago
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    Right!

  18. El_Arrow
    • one year ago
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    so you dont do the 1/n/n/n * 3^n/n thing?

  19. El_Arrow
    • one year ago
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    nvm

  20. El_Arrow
    • one year ago
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    thanks both of you

  21. Astrophysics
    • one year ago
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    Np :)

  22. freckles
    • one year ago
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    ditto

  23. Astrophysics
    • one year ago
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    I have a quick question though, when we do limits, shouldn't we let n = x, otherwise it's not a function, I remember something like that...

  24. zzr0ck3r
    • one year ago
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    In general we are using \(n\) for sequenes and \(x\) for real numbers, but a sequence is just a function from the naturals.

  25. Astrophysics
    • one year ago
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    Right!

  26. freckles
    • one year ago
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    \[\text{ \let } f: \mathbb{R} \rightarrow \mathbb{R} \text{ be defined by } f(n)=n^2 \] you can use n or any letter there to represent the input.

  27. Astrophysics
    • one year ago
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    Alright, thank you :)

  28. zzr0ck3r
    • one year ago
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    Here I assume you have a sequence and you are to have as inputs 1,2,3,4,5....

  29. zzr0ck3r
    • one year ago
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    same answer either way...

  30. zzr0ck3r
    • one year ago
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    42

  31. Astrophysics
    • one year ago
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    A 9+10 reference and hitchhikers guide in the same post, welp...

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