Question

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

Answer 1

We have,

$\underset{x\to 3}{lim}\frac{x^n-3^n}{x-3}=108$

Now,

$\Rightarrow n{\left(3\right)}^{n-1}=108$

$=4\times {\left(3\right)}^3$

$n=4$

Hence, this is the answer.