Hyperbolic functions

  • Thread starter nameVoid
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  • #1
241
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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
 

Answers and Replies

  • #2
Gib Z
Homework Helper
3,346
5
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.
 
  • #3
241
0
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)
 
  • #4
241
0
[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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