Question

If $\underset{x\to 3}{lim}\frac{x^n-3^n}{x-3}=108$, find the value of n.

Answer 1

Using formula $\underset{x\to a}{lim}\frac{x^n-a^n}{x-a}=n.a^{n-1}$

$\underset{x\to 3}{lim}\frac{x^n-3^n}{x-3}=n{.3}^{4-1}={4.3}^3$

$n=4$