Question

$\underset{x\to 1}{lim}\frac{x^8-2x+1}{x^4-2x+1}$ equals

• A. $3$
• B. $0$
• C. $-3$
• D. $1$

Answer 1

The correct option is A $3$

We have,
$\underset{x\to 1}{lim}\frac{x^8-2x+1}{x^4-2x+1}$

$=\underset{x\to 1}{lim}\frac{(x-1)(x^7+x^6+x^5+x^4+x^3+x^2+x-1)}{(x-1)(x^3+x^2+x-1)}$

$=\underset{x\to 1}{lim}\frac{x^7+x^6+x^5+x^4+x^3+x^2+x-1}{x^3+x^2+x-1}=\frac{6}{2}=3$