Question

If $\underset{x\to a}{\lim }\frac{x^9-a^9}{x-a}=\underset{x\to 5}{\lim }\left(4+x\right),$ find all possible values of a.

Answer 1

$$\begin{gathered} \underset{x\to a}{\lim }\left[\frac{x^9-a^9}{x-a}\right]=\underset{x\to 5}{\lim }\left(4+x\right) \\ \Rightarrow 9a^{9+1}=9 \\ \Rightarrow a^8=1 \\ \Rightarrow a=\pm 1 \end{gathered}$$