Answer
$3$
Work Step by Step
Factor each polynomial:
$\lim _{x\rightarrow 1}\dfrac {x^{3}-1}{x-1}
\\=\lim _{x\rightarrow 1}\dfrac {\left( x-1\right) \left( x^{2}+x+1\right) }{x-1}$
Cancel the common factors:
$\\=\lim _{x\rightarrow 1}\left( x^{2}+x+1\right)
\\=1^{2}+1+1
\\=3$
