Question

Помогите с решением производной

Answer 1

4)

$\lim_{x \to \infty} \frac{2x^2-4x+5}{x^3+4}|:x^3= \lim_{x \to \infty} \frac{\frac{2}{x}-\frac{4}{x^2}+\frac{5}{x^3}}{1+\frac{4}{x^3}} = [\frac{1}{x^n} \to 0, x \to \infty] = \lim_{x \to \infty}\frac{0}{1}=0.$

5)$\lim_{x \to \infty} \frac{8x^3-3x^2-2x}{4x^2-2x+1}|:x^3= \lim_{x \to \infty} \frac{-\frac{3}{x}-\frac{2}{x^2}+8}{\frac{4}{x}-\frac{2}{x^2}+\frac{1}{x^3}} = [\frac{1}{x^n} \to 0, x \to \infty] = \lim_{x \to \infty}\frac{8}{0}=\infty.$