Question

Solve:-
$\underset{x\to 2}{lim}\frac{x^n-2^n}{x-2},n\in N$

Answer 1

Now,

$\underset{x\to 2}{lim}\frac{x^n-2^n}{x-2},n\in N$ $\left(\frac{0}{0}form\right)$

Now applying L'Hospital's rule we get,

$=\underset{x\to 2}{lim}n{x}^{n-1}$

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