Granične vrednosti

Limes zbira i razlike $$\lim (f\pm g)=\lim f\pm \lim g$$

Limes proizvoda $$\lim (f\cdot g)=\lim f\cdot \lim g$$

Limes količnika $$\lim \frac{f}{g}=\frac{\lim f}{\lim g}$$

Poznate granične vrednosti

  • \(\lim \limits_{x \to 0 }a^x=1\)
  • \(\lim \limits_{x \to \infty }\left ( 1+\frac{a}{x} \right )^x=e^a\)
  • \(\lim \limits_{x \to \infty }\frac{x^n}{n!}=0\)
  • \(\lim \limits_{x \to \infty }\frac{x}{\sqrt[x]{x!}}=e\)
  • \(\lim \limits_{x \to 0 }\frac{\sin x}{x}=1\)
  • \(\lim \limits_{x \to 0 }\frac{\tan x}{x}=1\)
  • \(\lim \limits_{x \to \infty }\frac{x!}{x^xe^{^-x}\sqrt{x}}=\sqrt{2\pi }\)