Question

lim x→∞ x⁴-x²+2/x³-x+1. Как решить?

Answer 1

$\displaystyle \lim_{x \to \infty} \frac{x^4-x^2+2}{x^3-x+1}= \lim_{x \to \infty} \frac{ \frac{x^4}{x^4}- \frac{x^2}{x^4}+ \frac{2}{x^4}}{ \frac{x^3}{x^4}- \frac{x}{x^4}+ \frac{1}{x^4}}= \lim_{x \to \infty} \frac{1- \frac{1}{x^2}+ \frac{2}{x^4}}{ \frac{1}{x}- \frac{1}{x^3}+ \frac{1}{x^4}}=$
$\displaystyle = \lim_{x \to \infty} \frac{1-x^{-2}+2 \cdot x^{-4}}{x^{-1}-x^{-3}+x^{-4}}= \frac{1-0+0}{0-0+0}= \frac{1}{0}= \infty$