Question

lim x→∞ x⁴-x²+2/x³-x+1. Как решить?

Answer 1

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