Re: Graph?

From: David W. Cantrell (DWCantrell_at_sigmaxi.org)
Date: 12/06/04 

Date: 06 Dec 2004 13:01:03 GMT

"mike3" <mike4ty4@yahoo.com> wrote:
>
> What does the graph of Imag(x^x) for x < 0 look like?

Wasn't that already answered in your recent thread "The function x^x"?

There, I suggested that, for x < 0, Imag(x^x) be rewritten as

  (-x)^x * sin(pi*x)

which can be easily graphed for x < 0. Doing so, you will see that the
graph oscillates about the negative x-axis with rapidly decreasing
amplitude as we move farther from the origin. Of course, the graphs of
-(-x)^x and (-x)^x form an envelope for the graph in question, and the
oscillation is due to the sine factor.

David

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