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Hyperbolic functions

  • Thread starter Brewer
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212
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[SOLVED] Hyperbolic functions

As part of a long winded "show that" question I've ended up at the point where I have [tex]xcothx[/tex] and I want to show that this is equal to [tex]cothx - \frac{1}{x}[/tex] only I have no ideas how to get there. I can't see any reason why this should be so, but I'm pretty confident that I'm correct so far (in fact I know I am!).

Obviously I could take the "magic step" when doing this kind of question (in that I could just write the final answer down, and hope that I'm close enough for this step to be intuitive) but I'd quite like to know the step to take.

Thanks in advance guys.
 

Answers and Replies

tiny-tim
Science Advisor
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erm … when x = 1, xcothx = coth1, but cothx - 1/x = coth1 - 1 … so they're not equal. :frown:

How did you get to that position?
 
HallsofIvy
Science Advisor
Homework Helper
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Well, you aren't going to be able to prove that because it pretty obviously isn't true. In particular, you would be proving, taking x= 1, that coth(1)= coth(1)- 1 which can't be true.
 
212
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Meh, so the guy I checked my working with up until now is wrong.

So what I did is
[tex]
U=-\frac{d(lnZ)}{d\beta}[/tex]
[tex]=-\frac{1}{z}\frac{dZ}{d\beta}[/tex]
[tex]=\frac{-\beta \mu B}{sinh(\beta \mu B)}(\mu Bcosh(\beta \mu B)[/tex]
[tex]=-\frac{\mu ^2 B^2 \beta cosh(\beta \mu B)}{sinh(\beta \mu B)[/tex]
[tex]=-\mu B(\beta \mu Bcoth(\beta \mu B)[/tex]


where [tex]Z = \frac{sinh(\beta \mu B)}{\beta \mu B}[/tex]

Are there problems with what I've done then?
 
Last edited:
212
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I've tried to correct the latex, but if it hasnt come out properly then the line thats gone wrong is the unfactorised form of the final line
 
212
0
Solved. Helps when you remember your quotient rule
 

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