Do you know your abcs?

Calculus Level 3

\[ \mathscr{E}=\displaystyle \lim_{(a,b,c)\to(1,1,1) }\dfrac{a^3 + b^3 + c^3 -3abc}{a^2 +b^2 +c^2 - ab- ac -bc} \]

Find \( \mathscr{E}\).

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