Question

If $\underset{x\to a}{\lim }\frac{x^9-a^9}{x-a}=9,$ find all possible values of a.

Answer 1

$$\begin{gathered} \underset{x\to a}{\lim }\left[\frac{x^9-a^9}{x-a}\right]=9 \\ \Rightarrow 9a^8=9 \\ \Rightarrow a^8=1 \\ \Rightarrow a=\pm 1 \end{gathered}$$