Granice funkcji:

$$\operatorname{}{a^{x} = \left\{ \begin{matrix} + \infty\ dla\ a > 1 \\ 0\ dla\ a\epsilon(0,1) \\ \end{matrix} \right.\ }$$

$$\operatorname{}{a^{x} = \left\{ \begin{matrix} 0\ dla\ a > 1 \\ + \infty\ dla\ a\epsilon(0,1) \\ \end{matrix} \right.\ }$$

e^x =   + ∞

e^x =  0

lnx =   + ∞

lnx =   − ∞

$$\operatorname{}{arctgx = \ \frac{\pi}{2}}$$

$$\operatorname{}{arctgx = \ - \frac{\pi}{2}}$$

$$\operatorname{}{\frac{\sin{f(x)}}{f(x)} = 1}$$

$$\operatorname{}{\frac{\operatorname{tgx}{f(x)}}{f(x)} = 1}$$

$$\operatorname{}{\frac{\sin x}{x} = 1}$$

$$\operatorname{}{\frac{\operatorname{tg}x}{x} = 1}$$

$$\operatorname{}{{(1 + f(x)}^{\frac{1}{f(x)}} = e}$$

Logarytm naturalny:

ln x = e

Ale gdy masz równania typu: (gdzie a ϵR)

ln x =a ln x >a ln x <a

x= e^a x> e^a x< e^a

Przykład:
ln x= - $\frac{3}{4}$

x = $e^{- \frac{3}{4}}$