Answer
$3a^2$
Work Step by Step
We have to determine $L=\lim\limits_{x \to a}\dfrac{x^3-a^3}{x-a}$.
Factor the numerator using the identity:
$x^3-y^3=(x-y)(x^2+xy+y^2)$:
$L=\lim\limits_{x \to a}\dfrac{(x-a)(x^2+ax+a^2)}{x-a}$
Simplify:
$L=\lim\limits_{x \to a} (x^2+ax+a^2)
Determine $L$:
$L=a^2+a^2+a^2=3a^2$
