Answer
$3$
Work Step by Step
Factor each polynomial:
$\lim _{x\rightarrow 2}\dfrac {x^{3}-8}{x^{2}-4}
\\=\lim _{x\rightarrow 2}\dfrac {x^{3}-2^{3}}{x^{2}-2^{2}}
\\=\lim _{x\rightarrow 2}\dfrac {\left( x-2\right) \left( x^{2}+2x+2^{2}\right) }{\left( x-2\right) \left( x+2\right) }$
Cancel the common factors:
$\\=\lim _{x\rightarrow 2}\dfrac {\left( x^{2}+2x+4\right) }{x+2}
\\=\dfrac {2^{2}+2\times 2+4}{2+2}
\\=\dfrac {12}{4}
\\=3$
