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Math Help - Csc Limit question

  1. #1
    Senior Member polymerase's Avatar
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    Csc Limit question

    Find f'(\frac{\pi}{4}) if f(x)=\lim_{t\to{x}}\frac{csc\;t -csc\;x}{t-x}
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by polymerase View Post
    Find f'(\frac{\pi}{4}) if f(x)=\lim_{t\to{x}}\frac{csc\;t -csc\;x}{t-x}
    note that f(x) is defined by the limit definition of the derivative of \csc x

    thus, let g(x) = \csc x

    we have that f(x) = g'(x)

    so f'(x) = g''(x)

    therefore, f' \left( \frac {\pi}4 \right) = g'' \left( \frac {\pi}4 \right)

    now find g''(x) and you will have your answer


    are you required to find the derivative by evaluating the limit? i doubt it. it will especially be a pain doing it for the second derivative
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  3. #3
    Senior Member polymerase's Avatar
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    Quote Originally Posted by Jhevon View Post
    note that f(x) is defined by the limit definition of the derivative of \csc x

    thus, let g(x) = \csc x

    we have that f(x) = g'(x)

    so f'(x) = g''(x)

    therefore, f' \left( \frac {\pi}4 \right) = g'' \left( \frac {\pi}4 \right)

    now find g''(x) and you will have your answer


    are you required to find the derivative by evaluating the limit? i doubt it. it will especially be a pain doing it for the second derivative
    maybe im just doing it wrong but i'm getting \sqrt{2}+\sqrt{8} and thats not right
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