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Hyperbolic functions

  1. Sep 28, 2009 #1
    Find the points on the graph of y=sinhx at which the tangent line has slope 2

    dy/dx=coshx=2

    (e^x+e^(-x))=4
    x-x=ln4
     
  2. jcsd
  3. Sep 28, 2009 #2

    Gib Z

    User Avatar
    Homework Helper

    You have used an incorrect property of logarithms.

    [tex] \log (a+b) \neq \log a + \log b[/tex].

    There is no "useful" property for the log of a sum.

    For solve that equation you have, try thinking about how you can make that a quadratic equation in e^x.
     
  4. Sep 29, 2009 #3
    y=sinhx
    y'=coshx=2
    cosh^2x-sinh^2x=1
    sinh^2=3
    sinhx=+||-3^(1/2)=(e^x-e^(-x))/2
    e^x-e^(-x)=+||-2*3^(1/2)
    x=ln(+||-2*3^(1/2))/2
    y=+||-e^(1/2)
     
  5. Sep 29, 2009 #4
    [tex]
    \frac{d}{dx}sinhx=coshx=2
    [/tex]
    [tex]
    cosh^2x-sinh^2x=1=4-sinh^2x
    [/tex]
    [tex]
    sinhx=3^{1/2}
    [/tex]
    [tex]
    sinhx=-3^{1/2}
    [/tex]
    [tex]
    sinhx=\frac{e^x-e^{-x}}{2}=3^{1/2}
    [/tex]
    [tex]
    e^x-e^{-x}=2*3^{1/2}
    [/tex]
    [tex]
    2x=ln2+ln(3^{1/2})
    [/tex]
    [tex]
    x=\frac{ln2+ln(3^{1/2})}{2}
    [/tex]
    using the same methods for sinhx=-3^(1/2) does not work since taking the natural log of -sqrt3 this probelms should be solvable without inverses
     
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