Question

$\underset{x\to a}{\lim }\frac{x^{2/7}-a^{2/7}}{x-a}$

Answer 1

$$\begin{gathered} \underset{x\to a}{\lim }\left[\frac{x^{{\displaystyle \frac{2}{7}}}-a^{{\displaystyle \frac{2}{7}}}}{x-a}\right] \\ =\frac{2}{7}{a}^{\frac{2}{7}-1}\left[\because \underset{x\to a}{\lim }\left[\frac{x^n-a^n}{x-a}\right]=n{a}^{n-1}\right] \\ =\frac{2}{7}{a}^{-\frac{5}{7}} \end{gathered}$$