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Plot obliterates its y-axis !?


Yesterday, Tim Trudgian posted a query about finding a maximum
of a particular function.
He mentioned two plots:

Plot[Abs[Zeta[1/2 + I*t]/t^(1/4)], {t, 3, 10^5}, PlotRange -> Full]
Plot[Abs[Zeta[1/2 + I*t]/t^(1/4)], {t, 3, 10^6}, PlotRange -> Full]

This led me to try this:

Plot[Abs[Zeta[1/2 + I*t]/t^(1/4)], {t, 35000, 50000}, PlotRange -> Full]

which (unlike the first two) seems to exhibit a bug in v9.0.1:
The area of the graph overwrites the area of the y-axis (tick marks and
labels).
Furthermore,

Plot[Abs[Zeta[1/2 + I*t]/t^(1/4)], {t, 35000, 45000}, PlotRange -> Full]

yields an even uglier plot (if that can be possible).
What is going on here?




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