If $$\displaystyle\lim_{x\rightarrow 3}\dfrac{x^n-3^n}{x-3}=108$$, find the value of n.
Correct option is A. 4
Using formula $$\displaystyle \lim_{x\rightarrow a}{\dfrac{x^n-a^n}{x-a}}=n.a^{n-1}$$
$$\displaystyle \lim_{x\rightarrow 3}{\dfrac{x^n-3^n}{x-3}}=n.3^{4-1}=4.3^3$$
$$n=4$$