Re: (Cos x)^x plot Message #4 Posted by Karl Schneider on 1 Dec 2007, 2:19 p.m., in response to message #3 by Chuck
Hi, Chuck 
Thank you for the plot, which would be laborious to produce using an HP15C and graph paper...
Quote:
It's actually defined when negative, as long as the values aren't complex.
The function is defined continuously in the real domain for positive or negative x as long as "cos x" is positive. If "cos x" is negative, then only integer values of x can produce a realvalued result.
Quote:
Also, it resembles secant for x<0.
Since cosine is "even", [cos x = cos(x)], for negative x we can write
(cos x)^{x} = 1 / [(cos x)^{x}
Of course, sec x = 1 / cos x.
Quote:
The spikes and "U"'s get narrower for large x's.
As expected, since larger exponents "reduce" smaller arguments. That is, x^{a} < x for x < 1 and a > 1.
I understand the solid lines of the plot, where the function has a realvalued result, but the dotted parts (e.g., between pi/2 < x < 3*pi/2) don't seem to represent Re[f(x)].
 KS
Edited: 1 Dec 2007, 3:35 p.m.
