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Mathematics

Fixed Point of E^x=Cos(x)

erinleigh098
Posted 11 years ago

I do not understand how to find the fixed point of a problem in mathematica. I need to find the fixed point of e^x=cosx and I am stuck. If anyone understands fixed points that would be very helpful. thanks

POSTED BY: erinleigh098
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Funny thing: by accident I typed in the following

Plot[Exp[-x] == Cos[x], {x, -1, 10}, PlotLabel -> "Plot[Exp[-x]==Cos[x]]"]

enter image description here

Which is different from

Plot[{Exp[-x], Cos[x]}, {x, -1, 10},  PlotLabel -> "Plot[{Exp[-x],Cos[x]}]"]

enter image description here

Normally I would expect a == b to be a logical expression which is either True or False.

Any explanation for the strange behaviour discovered by accident?

Regards, Wolfgang
POSTED BY: Dr. Wolfgang Hintze

I get an empty plot in Mathemaca 10 running under Linux.
POSTED BY: Daniel Lichtblau

Must be a peculiarity of 

$Version

(* Out[40]= "8.0 for Microsoft Windows (64-bit) (October 7, 2011)" *)

In 5.2 for Microsoft Windows x86 (64 bit) (June 20, 2005), which I still keep on my PC (you will remember; it is much faster doing Integrate than Version 8) I get the error message "Plot::plnr : Exp[-x] == Cos[x] is not a machine size real number at x = -1 ..." and an empty Plot which is correct.
POSTED BY: Dr. Wolfgang Hintze

Thanks, Daniel, for pointing out this site to me.

It seems, however, that in contrast to StackExchangeMMA Latex is not supported here. Example:

$\sqrt{1+x^2}$

Or am I doing something wrong?

I have gradually become acustomed to using it for better readability in texts.

Regards, Wolfgang
POSTED BY: Dr. Wolfgang Hintze
POSTED BY: Daniel Lichtblau
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