Question

The value of $\underset{x\to 1}{lim}\frac{x^7-2x^5+1}{x^3-3x^2+2}$ is.

• A. $0$
• B. $1$
• C. $-1$
• D. None of these

Answer 1

The correct option is B $1$

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