Sunday, 31 August 2014

Limits problem: Factoring a cube root of x?



Disclaimer: I am an adult learning Calculus. This is not a student posting his homework assignment. I think this is a great forum!



$$\lim_{x\to8}{\frac{\sqrt[3] x-2}{x-8}}$$



How do I factor the top to cancel the $x-8$ denominator?


Answer




Actually you need to factor the denominator: $x-8 = (\sqrt[3]{x})^3-2^3 = (\sqrt[3]{x}-2)\left((\sqrt[3]{x})^2+2\sqrt[3]{x}+2^2\right)$.


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