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    (Original post by The Bachelor)
    This is kind of circular, as you require the limit to prove the derivative is cos in the first place.
    You're joking right?
    Care to read the rest of the thread? Or at least a few posts above yours? :p:
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    (Original post by Drederick Tatum)
    sin x is usually defined as the limit x-(x^3)/3!+(x^5)/5! -...
    (so sin x is well defined for all real x by, for example, the ratio test)
    Then, by writing out the function (sin x)/x using the definition of sin x, the proof that (sin x)/x tends to 1 as x tends to zero is clear.
    This might be circular, as deriving the series requires knowledge of the derivative. However, I suppose one can also derive the unit circle properties starting from the series as the definition.
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    (Original post by SimonM)
    Ok, so why do you go on to proceed with invalid and irrelevant arguments involving the theory of education?
    This is getting tiresome. The OP did not know about L'Hopital's Rule. Now she knows about L'Hopitals' Rule. That is not a bad thing.

    You suggested there is a "proper" way for each mathematical topic to be taught and that was the statement I was challenging. I was not attempting to defend the use of L'Hopital. A knowledge of educational theory is relevant as you have very little understanding of the way people learn. It is very individual (look up Howard Gardner) and quality learning routinely occurs in the absence of any teaching at all.

    Please ignore the other stuff I said. I had a difficult week and am somewhat preoccupied.
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    (Original post by Horizontal 8)
    You're joking right?
    Care to read the rest of the thread? Or at least a few posts above yours? :p:

    Are you arguing that it is not circular, or that you don't care?

    Most of the time, this limit is only used when trying to figure out the derivative of sin. So it doesn't really make sense to go "oh the derivative of sin is cos so i'll just use L'hopital's rule and here's the limit and thereby I prove the derivative of sin is cos."

    (In fact, it doesn't make sense in any other situation, but here it blatantly does not make sense.)
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    (Original post by Mr M)
    This is getting tiresome. The OP did not know about L'Hopital's Rule. Now she knows about L'Hopitals' Rule. That is not a bad thing.

    You suggested there is a "proper" way for each mathematical topic to be taught and that was the statement I was challenging. I was not attempting to defend the use of L'Hopital. A knowledge of educational theory is relevant as you have very little understanding of the way people learn. It is very individual (look up Howard Gardner) and quality learning routinely occurs in the absence of any teaching at all.

    Please ignore the other stuff I said. I had a difficult week and am somewhat preoccupied.
    OK, I realise that I phrased that statement badly. I also accept that Hathalan learning L'Hopital's rule is a benefit for a different reason. I will indeed have a look at the references mentioned.

    No hard feelings?
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    Most of the proofs in this thread are circular.

    (I'll get my coat.)
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    (Original post by SimonM)
    OK, I realise that I phrased that statement badly. I also accept that Hathalan learning L'Hopital's rule is a benefit for a different reason. I will indeed have a look at the references mentioned.

    No hard feelings?
    Absolutely not.
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    (Original post by Glutamic Acid)
    Most of the proofs in this thread are circular.

    (I'll get my coat.)
    That was actually quite good.
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    (Original post by The Bachelor)
    Are you arguing that it is not circular, or that you don't care?

    Most of the time, this limit is only used when trying to figure out the derivative of sin. So it doesn't really make sense to go "oh the derivative of sin is cos so i'll just use L'hopital's rule and here's the limit and thereby I prove the derivative of sin is cos."

    (In fact, it doesn't make sense in any other situation, but here it blatantly does not make sense.)
    Neither I'm just pointing out that the point you brought up was in great discussion already :p: Thanks for the insight nevertheless.
 
 
 
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