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nickymarden

  • 2 years ago

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  1. nickymarden
    • 2 years ago
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    \[\lim_{x \rightarrow 0} cosx-1/x\]

  2. Thomas9
    • 2 years ago
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    cos(x-1/x)?

  3. nickymarden
    • 2 years ago
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    (cosx-1)/x

  4. Thomas9
    • 2 years ago
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    I had my answer ready for the other one, I need to think about this one.

  5. TuringTest
    • 2 years ago
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    are you allowed to use l'Hospitals rule?

  6. nickymarden
    • 2 years ago
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    nope. Professor said that if we use it he won't consider the answer

  7. TuringTest
    • 2 years ago
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    well this limit is very well-known, and is usually proven geometrically, so... I'm not sure what we want to do here

  8. nickymarden
    • 2 years ago
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    there are 2 ways to finding the answer, and I know it's 0. I know one of them, wich takes too long, i want the other.

  9. Thomas9
    • 2 years ago
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    You can write cos(x) as a series, that'll work.

  10. TuringTest
    • 2 years ago
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    ^that is true, that would be the only other way to prove it besides the geometric way which is given here: http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-a-definition-and-basic-rules/session-7-derivatives-of-sine-and-cosine/

  11. TuringTest
    • 2 years ago
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    so there are technically 3 ways of finding the answer

  12. nickymarden
    • 2 years ago
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    yep. MIT always saving my life. Thanks again :P

  13. TuringTest
    • 2 years ago
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    that is the long way though^ the "short" way is l'Hospitals rule

  14. TuringTest
    • 2 years ago
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    but you're welcome :)

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