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Thread: Quick question about fractional derivatives and is Latex broken?

  1. Top | #11
    Quantum Hot Dog Kharakov's Avatar
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    Let's take a simple example. f(x)=x + c f '(x)=1

    How, is the derivative local, if any value of f(x) can have the same derivative? lol... this one is funny.

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    Elder Contributor barbos's Avatar
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    Quote Originally Posted by Kharakov View Post
    Let's take a simple example. f(x)=x + c f '(x)=1

    How, is the derivative local, if any value of f(x) can have the same derivative? lol... this one is funny.
    What is wrong with you?

  3. Top | #13
    Quantum Hot Dog Kharakov's Avatar
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    Quote Originally Posted by barbos View Post
    Quote Originally Posted by Kharakov View Post
    Let's take a simple example. f(x)=x + c f '(x)=1

    How, is the derivative local, if any value of f(x) can have the same derivative? lol... this one is funny.
    What is wrong with you?
    My sense of humor. Know its knot.

  4. Top | #14
    Administrator lpetrich's Avatar
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    Finite-difference formulas are approximations for derivatives, not exact expressions. But there are exact formulas.

    For integration, f(-n)(x) = 1/((n-1)!) int of (x - t)n-1 f(t) by t from t0 to x

    For differentiation, f(n)(x) = n!/(2*pi*i) contour int of f(t) / (t - x)n+1 by t around x

    One can use them to find fractional-derivative formulas, using the Euler gamma function to extend the factorial function to fractional args.

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    The Tech Guy RayJ's Avatar
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    Quote Originally Posted by Kharakov View Post
    Latex broken?
    Latex is fixed!

  6. Top | #16
    Administrator lpetrich's Avatar
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    Repeated integration:
     f^{(-n)}(x) = \frac{1}{(n-1)!} \int_{t_0}^x (x - t)^{n-1} f(t) dt

    Repeated differentiation:
     f^{(n)}(x) = \frac{n!}{2\pi i} \oint \frac{f(z)}{(x-z)^{n+1}} dz

    a contour integral, where the contour goes around x.

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    Quote Originally Posted by Kharakov View Post
    ...if no forum user is wearing latex...
    I am wearing latex.

    I always wear two condoms wherever I go. If I happen to find myself in a situation where I am about to have sex with someone, I remove one of the condoms... and boy, does it feel GREAT!

  8. Top | #18
    Quantum Hot Dog Kharakov's Avatar
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    "I am wearing latex" was great to read, until I got to the part where you wear condoms. Thanks for the image. It will definitely help out in the future, when I don't want to hook up with a hot woman. Ok. It won't help in the future. I'm not going to have that chance. lol.

    You're the first person I've spoke with who needed 2 condoms. Is it a genetic condition, or is one of them your gun?

    I thought Inspector Sledgehammer was the only person who protected their gun during sex.

  9. Top | #19
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    Quote Originally Posted by Kharakov View Post
    "I am wearing latex" was great to read, until I got to the part where you wear condoms. Thanks for the image. It will definitely help out in the future, when I don't want to hook up with a hot woman. Ok. It won't help in the future. I'm not going to have that chance. lol.

    You're the first person I've spoke with who needed 2 condoms. Is it a genetic condition, or is one of them your gun?

    I thought Inspector Sledgehammer was the only person who protected their gun during sex.
    no, the point is that with two condoms on, I can't feel a damn thing... so when I take one off, I'm SUPER sensitive and it feels great.

    dumb joke originally intended to poke fun at those that say that they hate condoms because they numb the sensations.. which of course they do... So I say that (not only do I wear one...) I wear two!

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