Question

If ${lim}_{x\to 3}\frac{x^n-3^n}{x-3}=108,$ then the value of $n$ is

• A. $2$
• B. $3$
• C. $8$
• D. $4$

Answer 1

The correct option is D $4$

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

Applying L'Hospital Rule

$\underset{x\to 3}{lim}n{x}^n-1=108⟹n(3{)}^{n-1}=4(3{)}^3$

So $n=4$