Goal: Reason regarding the BiotSavart law
Source: 283650 B from an infinite wire.
If B = μ_{0}I/4πD at point P which is a distance D from
the end of a “halfinfinite” wire, then what would be the magnetic field
at P if the wire went to infinity in both directions?
 It would be 0 because the leftportion of the wire would cancel the
magnetic field from the rightportion of the wire. 
It would be twice the answer above.

It is not 0, but it is also not twice the answer above – you have some
cancellation and you need to figure it out putting in the appropriate
sines and cosines.
Commentary:
Answer
(2) This question is only of value if one has obtained the field at the
end of a semiinfinite wire by direct integration. It is important for
students to recognize situations where the BiotSavart Law must be used
versus cases where Ampere’s Law can be used.