## Různé limity

### Úloha číslo: 2963

Spočtěte limity

• #### Varianta 1

$$\displaystyle \lim_{x\to 0}\frac{\sin x}{2x}$$

• #### Varianta 2

$$\displaystyle \lim_{x\to 0}\frac{\sin(\sin (\sin x))}{\hbox{tg}(\hbox{tg}(x))}$$

• #### Varianta 3

$$\displaystyle \lim_{x\to 0}\frac{\hbox{tg}(x) - \sin(x)}{x^3}$$

• #### Varianta 4

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

• #### Varianta 5

$$\displaystyle \lim_{x\to \infty}x\sin{\left( \frac1x\right)}$$

• #### Varianta 6

$$\displaystyle \lim_{x\to 0}\frac{a^x - 1}{x}, a > 0$$

• #### Varianta 7

$$\displaystyle \lim_{x\to e}\frac{\ln x - 1}{x - e}$$

• #### Varianta 8

$$\displaystyle \lim_{x\to 0^+}\frac{e^{\sqrt{\sin x}} - \cos x}{\sqrt x}$$

• #### Varianta 9

$$\displaystyle \lim_{x\to \infty} \sqrt{x + \sqrt{x + \sqrt x}} - \sqrt x$$

• #### Varianta 10

$$\displaystyle \lim_{x\to 0} \frac{\cos\left(\frac{\sin x}x\right)} {1 + \cos\left(\frac{\sin^2 x}{x^2}\right)}.$$

• #### Varianta 11

$$\displaystyle \lim_{x \to 0} (x + 1)^{\frac1x}.$$