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anonymous

  • one year ago

limit as x approaches zero of quantity negative six plus x divided by x to the fourth power.

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  1. anonymous
    • one year ago
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    @Vocaloid

  2. anonymous
    • one year ago
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    \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\frac{6+x}{x^4}}\) this?

  3. anonymous
    • one year ago
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    yes!

  4. anonymous
    • one year ago
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    actually negative 6

  5. anonymous
    • one year ago
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    \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\frac{6+x}{x^4}}\) \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\frac{6}{x^4}+\lim_{x \rightarrow ~0}\frac{x}{x^4}}\) so I don't think you will get anything defined out of the limit

  6. anonymous
    • one year ago
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    wait, approaches -6?

  7. anonymous
    • one year ago
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    oh, -6+x! Doesn't matter

  8. anonymous
    • one year ago
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    you would be then getting \(\large \displaystyle \lim_{x \rightarrow ~0}\frac{-6}{x^4}+\frac{x}{x^4}\) and still DNE

  9. anonymous
    • one year ago
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    oh okay thanks!

  10. anonymous
    • one year ago
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    Wait so which one is it?

  11. anonymous
    • one year ago
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    it is infinity not zero, i think

  12. Vocaloid
    • one year ago
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    I don't believe L'Hopital's rule applies, -6/0 doesn't count as an indeterminate form

  13. anonymous
    • one year ago
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    no she meant part 2, but there x's xcancel

  14. anonymous
    • one year ago
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    What is that rule though?

  15. anonymous
    • one year ago
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    that is to differentiate top and bottom, IF you get 0/0 or ∞/∞, when you plug in the value that x approaches into the limit

  16. anonymous
    • one year ago
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    this is L'Hospital's Rule

  17. anonymous
    • one year ago
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    Could you guys help me with this?

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  18. anonymous
    • one year ago
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    So for example, I have: \(\large \displaystyle \lim_{x \rightarrow ~0}\frac{\sin(x)}{x}\) and there you would apply this rule (can you tell me why?)

  19. anonymous
    • one year ago
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    i don't see a reason for one-sided limit not to exist (unless the function is totally not on that interval, or if it goes into infinity - asymptote)

  20. Plasmataco
    • one year ago
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    Well x=2 is an asymptote

  21. Vocaloid
    • one year ago
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    @phunish well, it's asking for the limit as the function approaches x = 2 from the left, any ideas?

  22. anonymous
    • one year ago
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    ok, you see that the graph has two parts (two sticks :D) right/

  23. anonymous
    • one year ago
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    ?

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