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

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3You may use the limit definition of derivative, what is the derivative of \(\sqrt[3]{x+6}\) at \(x=2\) ?

elleblythe
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 we haven't started with derivatives yet so idk anything about them.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[\large \begin{align} \lim\limits_{x\to 2} \dfrac{2x}{2\sqrt[3]{x+6}}&=\lim\limits_{x\to 2} \dfrac{x2}{\sqrt[3]{x+6}2}\\~\\ &=\lim\limits_{x\to 2} \dfrac{(x+6)8}{\sqrt[3]{x+6}\sqrt[3]{8}}\\~\\ &=\lim\limits_{x\to 2} \dfrac{\left(\sqrt[3]{x+6}\right)^3\left(\sqrt[3]{8}\right)^3}{\sqrt[3]{x+6}\sqrt[3]{8}}\\~\\ \end{align}\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3next recall the identity \[a^3b^3 = (ab)(a^2+ab+b^2)\] expand the numerator
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