Question

If $li{m}_{x\to 2}$ $\frac{\left(x^n\right)-\left(2^n\right)}{x-2}$ =80 , where n is a positive integer,
then n=

• A. 3
• B. 5
• C. 2
• D. None of these

Answer 1

The correct option is B

5

$li{m}_{x\to 2}$ $\frac{\left(x^n\right)-\left(2^n\right)}{x-2}$ =n × $2^{n-1}$ ⇒ n × $2^{n-1}$ = 80 ⇒ n= 5