# Plot of $\sin(x^x)$ is missing from $x=143$

When plotting the graph of $\sin(x^x)$ I noticed that there is no plot from about $x=143$. I don't suppose there is a purely mathematical explanation for this?

So, why is there no graph in Mathematica from $x=143$? Some kind of overflow?

f[x_] = Sin[x^x]
Plot[{f[x]}, {x, 142, 144}, PlotStyle -> Thin, PlotLegends -> "Expressions"]


• Related: (3152), (104815) Feb 7 '16 at 12:27

Normally Plot uses machine precision numbers; your $x^x$ expression is hitting the limit of the numbers that can be represented in machine precision right about $x>143$.

Note:

Solve[\$MaxMachineNumber == x^x, x]

(* Out: {{x -> 143.016}} *)


You can increase the WorkingPrecision setting for Plot adequately, and the plot will be complete:

f[x_] = Sin[x^x]
Plot[{f[x]}, {x, 142, 144}, PlotStyle -> Thin, PlotLegends -> "Expressions",
WorkingPrecision -> 450]