What is the solution for: lim(x->2) (2-x)/(2-∛(x+6) The answer is supposed to be 12.

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What is the solution for: lim(x->2) (2-x)/(2-∛(x+6) The answer is supposed to be 12.

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You may use the limit definition of derivative, what is the derivative of \(\sqrt[3]{x+6}\) at \(x=2\) ?
@ganeshie8 we haven't started with derivatives yet so idk anything about them.
\[\large \begin{align} \lim\limits_{x\to 2} \dfrac{2-x}{2-\sqrt[3]{x+6}}&=\lim\limits_{x\to 2} \dfrac{x-2}{\sqrt[3]{x+6}-2}\\~\\ &=\lim\limits_{x\to 2} \dfrac{(x+6)-8}{\sqrt[3]{x+6}-\sqrt[3]{8}}\\~\\ &=\lim\limits_{x\to 2} \dfrac{\left(\sqrt[3]{x+6}\right)^3-\left(\sqrt[3]{8}\right)^3}{\sqrt[3]{x+6}-\sqrt[3]{8}}\\~\\ \end{align}\]

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next recall the identity \[a^3-b^3 = (a-b)(a^2+ab+b^2)\] expand the numerator

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