Question

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

Answer 1

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

Apply L-hospital rule, we get

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

Hence, this is the answer.