Evaluate \displaystyle\lim{x\to 2}\dfrac{x^3 - 8}{x - 2}.

12 x^3 - 8 = (x-2)(x^2 + 2x + 4). Cancel: x^2 + 2x + 4 \to 4 + 4 + 4 = 12.

Determining Limits Using Algebraic Manipulation

AP Calculus AB· difficulty 3/5

\displaystyle\lim_{x\to 2}\dfrac{x^3 - 8}{x - 2}

Explanation

x^3 - 8 = (x-2)(x^2 + 2x + 4)

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