Question

If ${lim}_{x\to 2}\frac{x^n-2^n}{x-2}=80$ and $n\in N$, find n.

Answer 1

${lim}_{x\to 2}\frac{x^n-a^n}{x-2}=80$

$\Rightarrow n{.2}^{n-1}=80$

$\Rightarrow n{.2}^{n-1}={5.2}^{5-1}$

$\Rightarrow n=5$