## Calculus 8th Edition

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.