======T17======
Pomocí l’Hospitalova pravidla vypočítejte limity:

=====199.=====
\( \lim_{x \to 0} \frac{\sin ax}{\sin bx} \)
[[wa> limit sin ax / sin bx as x-> 0]]

=====200.=====
\( \lim_{x \to 0} \frac{\cosh x - \cos x}{x^2} \)
[[wa> limit (cosh x - cos x)/x^2 as x->0 ]]
[[wa> derivative cosh x]] [[derivace#sinh]], použít pravidlo dvakrát!!!

=====201.=====
DELETEME \( \lim_{x \to 0} \frac{\tan x - x}{x - \sin x} \)
[[wa> limit of (tan x - x)/(x - sin x) as x->0 ]]

=====202.=====
DELETEME \( \lim_{x \to 0} \frac{3 \tan 4x - 12 \tan x}{2 \sin 4x - 12 \sin x} \)
[[wa> limit (3 tan 4x - 12 tan x)/(3 sin 4x - 12 sin x) as x->0 ]]


\( \lim_{x \to 0} \)

=====203.=====
DELETEME \( \lim_{x \to \frac{\pi}{2}} \frac{\tan 3x}{\tan x} =1/3 \), použít 3krát!
[[wa> limit tan 3x / tan x as x->pi/2 ]]



=====204.=====
DELETEME \( \lim_{x \to 0} \frac{x \cot x - 1}{x^2} \)

=====205.=====
DELETEME
\( \lim_{x \to \frac{\pi}{4}} \frac{\sqrt[3]{\tan x} - 1}{ 2 \sin^2 x - 1} \)

=====206.=====
DELETEME \( \lim_{x \to 0} \frac{x(e^x + 1) − 2(e^x − 1)}{x^3} \)


=====207.=====
\( \lim_{x \to 0} \frac{1 − \cos x^2}{x^2 sin x^2} \)
[[wa> limit (1 − cos x^2) / (x^2 sin x^2) as x->0 ]]

=====208.=====
\( \lim_{x \to 0} \frac{a^x - \a^{\sin x}}{x^3} \)

=====209.=====
\(   \lim_{x \to 1} \frac{x^x - x}{\ln x - x + 1} \)
[[wa> limit (x^x - x) / (ln x - x + 1) as x->1 ]]

=====210.=====
DELETEME \( \lim_{x \to 0} \frac{\ln \sin ax}{\ln \sin bx} \)
[[wa> limit of (ln sin ax)/(ln sin bx) as x->0 ]]

=====211.=====

=====212.=====
\( \lim_{x \to +\infty} \frac{x^n}{e^{ax}}, a>0, n>0 \)
[[wa> limit x^n/e^(ax) as x->+oo ]]

=====213.=====
\( \lim_{x \to 0} \frac{e^{-\frac{1}{x^2}}}{x^100} \)
[[wa> limit e^{-1/x^2 / x^100 as x->0 ]]

=====214.=====

=====215.=====
\( \lim_{x \to 1-} (ln x)(ln(1 - x) \)
[[wa> limit of (ln x)(ln(1 - x) as x->1- ]]

=====216.=====
DELETEME \( \lim_{x \to +0} x^a\ln x , a>0 \)
[[wa> limit x^a ln x as x->+0 ]]

=====217.=====
\( \lim_{x \to +0} x^x \)
[[wa> limit x^x as x->+0 ]]
[[wa>  derivative x^x ]] [[stepbystep#T217]]

=====218.=====
DELETEME
\( \lim_{x \to 0} x^(x^x - 1) \)
[[wa> limit x^(x^x - 1) as x->0 ]]

=====219.=====
\( \lim_{x \to 0} x^{x^x} - 1 \)
[[wa>  limit  of x^x^x -1 as x->0 ]]

[[wa>  derivative x^x ]] [[stepbystep#T219]]

=====220.=====
DELETEME \( \lim_{x \to +0} x^\frac{k}{1 + ln x} \)

=====221.=====
\( \lim_{x \to 1} x^\frac{1}{1 - x} \)
[[wa> limit x^(1/(1 - x)) as x->1 ]] [[stepbystep#T221]]

=====222.=====

=====223.=====

=====224.=====
DELETEME \( \lim_{x \to 0} (\cot x)^{\sin x} \)
[[wa> limit of (cotg x)^sin x as x->0 ]]

=====225.=====
\( \lim_{x \to 0+} (\ln \frac{1}{x})^x \)
[[wa> limit of (ln 1/x)^x as x->0+ ]] [[stepbystep#T225]]

=====226.=====

=====227.=====

=====228.=====
\( \lim_{x \to 1} ( \frac{1}{\ln x} - \frac{1}{x -1}) \)
[[wa> limit ( 1/ln x - 1/(x - 1) ) as x->1 ]]

=====229.=====

http://math.feld.cvut.cz/mt/txtb/5/txc3ba5d.htm [[derivace]]