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Question
\[\lim_{x \to a} \frac{x^{2/7} - a^{2/7}}{x - a}\]
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Solution
\[\lim_{x \to a} \left[ \frac{x^\frac{2}{7} - a^\frac{2}{7}}{x - a} \right]\]
\[ = \frac{2}{7} a^\frac{2}{7} - 1 \left[ \because \lim_{x \to a} \left[ \frac{x^n - a^n}{x - a} \right] = n a^{n - 1} \right]\]
\[ = \frac{2}{7} a^{- \frac{5}{7}}\]
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