= Solution
The <commutator> is $\boxed{[A,B]=AB-BA}$. To evaluate it for differential operators, apply it to a smooth test <wavefunction> $f$:
$$
[x,p_x]f=x(-i\hbar f')+i\hbar(xf)'=i\hbar f.
$$
Thus the <canonical commutation relation> is $\boxed{[x,p_x]=i\hbar I}$. The associated <Heisenberg uncertainty relation> is $\Delta x\,\Delta p_x\geq\hbar/2$. <Position> and <momentum> cannot both have arbitrarily sharp outcome distributions in the same prepared state, even with ideal measuring apparatus. This concerns quantum-state preparation, not merely a calibration error in a particular instrument.
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