I was looking at the graph of $$\frac{1}{x^x}=y^y+n$$ and found that it disappears at n greater than about $0.752$. What is the exact constant definition for n and why does the graph disappear (perhaps it becomes undefined or imaginary) at n greater than that?
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draw graphs of $y= x^x$ and then $y = \frac{1}{x^x}.$ I'm guessing you are using $x > 0$ http://www.printablepaper.net/category/graph – Will Jagy Sep 18 '15 at 20:20
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1yeah, min of $x^x$ occurs at $1/e,$ then write $A = \frac{1}{e^{1/e}} \approx 0.6922,$ then $\frac{1}{A} - A \approx 0.752$ – Will Jagy Sep 18 '15 at 20:27
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Aka $2 \sinh(1/e)$ :) – Alex Meiburg Feb 16 '16 at 12:42