Question

Evaluate using L-Hospital's rule
$\underset{x\to 1}{lim}\frac{x^7-2x^5+1}{x^3-3x^2+2}$

Answer 1

Using L-Hospitals's rule,we have

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

$=\underset{x\to 1}{lim}\frac{7x^6-10x^4}{3x^2-6x}$

$=\underset{x\to 1}{lim}\frac{7x^5-10x^3}{3x-6}$

$=\frac{7-10}{3-6}$

$=\frac{-3}{-3}=1$