#### Answer

0, please see step-by-step,

#### Work Step by Step

Finding the limit:
$\displaystyle \lim_{v\rightarrow c^{-}}(L_{0}\sqrt{1-\frac{v^{2}}{c^{2}}})=L_{0}\sqrt{1-1}=0$
Interpretation:
As the velocity approaches the speed of light,
the length of the object approaches $0$.
A left-sided limit is used because physically,
the right sided limit is not defined,
This is because velocity can not approach the speed of light from above (from the right):
$v\rightarrow c^{+}$ means $v > c$, which can not be.