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Решите задачу:

$\displaystyle \lim_{x \to a} \dfrac{x^\alpha-a^\alpha}{x^\beta-a^\beta}=\left\{\begin{array}{ccc}x-a=t\\ t\to0\end{array}\right\}=\lim_{t \to 0}\dfrac{a^{\alpha-\beta}((1+\frac{t}{a})^\alpha-1)}{(1+\frac{t}{a})^{\beta}-1}=\\ \\ =a^{\alpha-\beta}\lim_{t \to 0}\frac{\alpha\cdot\frac{t}{a}+o(t)}{\beta\cdot\frac{t}{a}+o(t)}=\frac{\alpha}{\beta}a^{\alpha-\beta}$