Question

If $\underset{x\to a}{\lim }\frac{x^5-a^5}{x-a}=405,$ find all possible values of a.

Answer 1

$$\begin{gathered} \underset{x\to a}{\lim }\left[\frac{x^5-a^5}{x-a}\right]=405 \\ \Rightarrow 5a^4=405 \\ \Rightarrow a^4=81 \\ \Rightarrow a^2=9 \\ \Rightarrow a=\pm 3 \end{gathered}$$