Answer
$4$
Work Step by Step
Factor each polynomial:
$\lim _{x\rightarrow 1}\dfrac {x^{4}-1}{x-1}
\\=\lim _{x\rightarrow 1}\dfrac {x^{4}-1^{4}}{x-1}
\\=\lim _{x\rightarrow 1}\dfrac {\left( x^{2}-1^{2}\right) \left( x^{2}+1^{2}\right) }{x-1}
\\=\lim _{x\rightarrow 1}\dfrac {\left( x-1\right) \left( x+1\right) \left( x^{2}+1^{2}\right) }{x-1}$
Cancel the common factors:
$\\=\lim _{x\rightarrow 1}\left( x+1\right) \left( x^{2}+1\right)
\\=\left( 1+1\right) \left( 1+1\right)
\\=2(2)
\\=4$
