Question

Find the following limit.
$\underset{x\to 2}{lim}\frac{x^4-3x+2}{x^5-4x+3}.$

Answer 1

$\underset{x\to 2}{lim}\frac{x^4-3x+2}{x^5-4x+3}=\frac{2^4-3\left(2\right)+2}{2^5-4\left(2\right)+3}=\frac{12}{27}=\frac{4}{9}$