The discussion focuses on evaluating the limit of the function (x^(1/3) - a^(1/3))/(x - a) as x approaches a. Participants suggest using the identity for the difference of cubes, (A^3 - B^3) = (A - B)(A^2 + AB + B^2), where A = x^(1/3) and B = a^(1/3), to factor out (x - a) from the numerator. An alternative method involves rationalizing the numerator by multiplying both the numerator and denominator by (x^(2/3) + a^(1/3)x^(1/3) + a^(2/3)). This approach effectively simplifies the limit evaluation.
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