= Solution
{c}
When both speeds are much smaller than $c$, expand the denominator of the <velocity-addition formula>:
$$
v''=(v+v')\left[1-\frac{vv'}{c^2}+O\!\left(\frac{v^2v'^2}{c^4}\right)\right],\qquad\boxed{v''\simeq v+v'.}
$$
This is the <Galilean transformation> limit. For $0\le\beta=v/c<1$ and $0\le\beta'=v'/c<1$,
$$
1-\frac{v''}c=\frac{(1-\beta)(1-\beta')}{1+\beta\beta'}>0.
$$
If both $v,v'\to c$ from below, the right side tends to zero, so
$$
\boxed{v''\to c\text{ from below}.}
$$
No sum of these subluminal speeds exceeds the <speed of light>.
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