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2bornot2b

  • 4 years ago

What are Cauchy’s first and second limit theorems?

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  1. precal
    • 4 years ago
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    http://www.saintjoe.edu/~karend/m441/Cauchy.html

  2. KingGeorge
    • 4 years ago
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    This paper seems to talk about them. It might take some time to read through, but it mentions the first and second theorems due to Cauchy, and provides analogues. http://plms.oxfordjournals.org/content/s2-5/1/206.full.pdf

  3. precal
    • 4 years ago
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    @KingGeorge I saw that one but it looked to technical, I posted a more historical explanation...... Oh Cauchy... the nightmares of my graduate program

  4. 2bornot2b
    • 4 years ago
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    @precal Can you please specify the theorems, I just can't find it in that long document of yours. And @KingGeorge you page is not opening for me, if you could post the theorems here, it would help a lot.

  5. precal
    • 4 years ago
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    do you have a calculus book around?

  6. KingGeorge
    • 4 years ago
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    I'll just attach the file. It's a real pain to write out.

  7. 2bornot2b
    • 4 years ago
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    Yes, I have but they are not specifying either. I mean there are several theorems, but which one is called the ................ I don't understand

  8. precal
    • 4 years ago
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    I found one reference but it is known as the mean value theorem

  9. KingGeorge
    • 4 years ago
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    It is a very technical paper, but it does mention "two well-known theorems" that were made by Cauchy.

  10. 2bornot2b
    • 4 years ago
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    Mean value theorem is not the same as cauchy's theorems are they?

  11. precal
    • 4 years ago
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    According to my calculus book, it states that the Genealized (or Cauchy's) Mean Value Theorem...... yes, it looks like it

  12. precal
    • 4 years ago
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    Cauchy did a lot of work in calculus.........like I said, "Nightmares of my graduate program"

  13. KingGeorge
    • 4 years ago
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    The mean value theorem doesn't really have to do with limits very much though... It doesn't seem like a "limit theorem" at least.

  14. 2bornot2b
    • 4 years ago
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    Anyway thanks

  15. KingGeorge
    • 4 years ago
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    If you look through the thing I posted, Thm. 1 is on the second page, Thm. 2 is on the 8th page.

  16. precal
    • 4 years ago
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    what derivatives don't have anything to do with limits??????? Let's see we teach limits first because they lead to derivatives, then we go to integration . Sorry to tell you, they are all related. A big spider web.

  17. KingGeorge
    • 4 years ago
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    They're definitely related, but I would hardly call it a limit theorem.

  18. precal
    • 4 years ago
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    ok I agree. You are right, they are listed there. I hope the asker can understand all of that :)

  19. KingGeorge
    • 4 years ago
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    It certainly doesn't help that the paper is 106 years old :/

  20. precal
    • 4 years ago
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    oh boy!!!

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