\lim _{ x\rightarrow 2 }{ \frac { { x }^{ 3 }-8 }{ { x }^{ 2 }-4 } } \\ \\ \indent = \lim_{x\rightarrow 2}{\frac {(x-2)(x^{2}+2x+4)}{(x+2)(x-2)}} \\ \\ \indent = \lim_{x\rightarrow 2}{\frac {x^{2}+2x+4}{x+2}} \\ \\ \indent = \frac {2^{2}+2(2)+4}{2+2} \\ \\ \indent = \frac {12}{4} \\ \\ \indent = 3