Evaluate the following limit: `lim_(x->a)(x^(2//7)-a^(2//7))/(x-a)`

Explanation

To evaluate the limit

\[ \lim_{x \to a} \frac{x^{2/7} - a^{2/7}}{x - a}, \]

we first notice that directly substituting \(x = a\) gives us the indeterminate form \(0/0\). Therefore, we can apply L'Hôpital's Rule, which states that if we have an indeterminate form \(0/0\) or \(\infty/\infty\), we can take the derivative of the numerator and the derivative of the denominator separately.

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