Question

If $li{m}_{x\to 2}\left[\frac{x^n-2^n}{x-2}\right]=32$, then find the value of n.

Answer 1

$li{m}_{x\to 2}\left[\frac{x^n-2^n}{x-2}\right]=n.2^{n-1}$

$n{.2}^{n-1}=32$

$n{.2}^{n-1}=4\times 8$

$n{.2}^{n-1}=4\times 2^{4-1}$

Therefore, $n=4$