Question

Найти производные функции

Answer 1

$1); ; limlimits _{x to infty}frac{x^2-5x^3}{x-2x^2+6x^3}=limlimits _{x to infty}frac{frac{1}{x}-5}{frac{1}{x^2}-frac{2}{x}+6}=-frac{5}{6}\\2); ; limlimits _{x to 0}frac{sin3x}{x}=limlimits _{x to 0}frac{3cdot sin3x}{3x}=3\\3); ; limlimits _{x to infty}Big (frac{x}{x-3}Big )^{x}=limlimits _{x to infty}Big (frac{x-3+3}{x-3}Big )^{x}=limlimits _{x to infty}Big (Big (1+frac{3}{x-3}Big )^{frac{x-3}{3}}Big )^{frac{xcdot 3}{x-3}}=$

$=e^{limlimits _{x to infty}frac{3x}{x-3}}=e^3$