\input amstex
\documentstyle{amsppt}
\parindent = 0 pt
\nopagenumbers
\overfullrule=0pt

\document
Urèete

$$\lim\limits_{x \to 0}{\sqrt{1+\tan x}-\sqrt{1-\tan x}\over \sin x}$$

\subheading{Øešení}
Platí

$${\sqrt{1+\tan x}-\sqrt{1-\tan x}\over \sin x}=
{{1+ \tan x - 1 + \tan x}\over \sin x [\sqrt(1+\tan x) + \sqrt(1-\tan x)]]}= 
{2 \over \cos x[\sqrt(1+\tan x) + \sqrt(1-\tan x)]}$$

Podle vìty o limitì spojité funkce se hledaná limita rovná 1.

\enddocument