Limits Level 2 Examples with difference of cubes IIT JEE AP Calculus

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why the other way round for the question ( x-2)/(cubic root x-cubic root 2) I mean cubing both numerator and denominator, does not work.

nadeenessa
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Wouldn't it have been easier to use L'hopital's rule in all of them? There would be questions where this method would be better suited but I don't see why the method would be used in this question over L'hopital's rule.

madhavmishra