## Limity podílů

### Úloha číslo: 3023

Určete následující limity

• #### Varianta 1

$$\displaystyle \lim_{x\to \infty}\frac{\ln x}{x}$$

• #### Varianta 2

$$\displaystyle \lim_{x\to 0}\frac{\ln(\cos x)}{x}$$

• #### Varianta 3

$$\displaystyle \lim_{x\to \infty}\frac{\ln(1+x^2)}{\ln(2+3x^3)}$$

• #### Varianta 4

$$\displaystyle \lim_{x\to 0}\frac{e^{x^2}-1}{\cos x-1}$$

• #### Varianta 5

$$\displaystyle \lim_{x\to 0^+}\frac{\ln(\sin2 x)}{\ln(\sin x)}$$

• #### Varianta 6

$$\displaystyle \lim_{x\to 0}\frac{\sin x}{\arcsin x}$$

• #### Varianta 7

$$\displaystyle \lim_{x\to 0}\frac{e^x-1}{\sin 2x}$$

• #### Varianta 8

$$\displaystyle \lim_{x\to \infty}\frac{e^{\sqrt{x}}}{x}$$

• #### Varianta 9

$$\displaystyle \lim_{x\to 0}\frac{\operatorname{tg} x}{\cos x-1}$$

• #### Varianta 10

$$\displaystyle \lim_{x\to \infty}\frac{\sin x-x}{x^3}$$

• #### Varianta 11

$$\displaystyle \lim_{x\to 0}\frac{\operatorname{arctg}(1+x)-\operatorname{arctg}(1-x)}{x}$$

• #### Varianta 12

$$\displaystyle \lim_{x\to 0}\frac{e^x\sin x-x(1+x)}{x^3}$$