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#LyX 2.3 created this file. For more info see http://www.lyx.org/
\lyxformat 544
\begin_document
\begin_header
\save_transient_properties true
\origin unavailable
\textclass article
\begin_preamble
\usepackage{siunitx}
\usepackage{pgfplots}
\usepackage{listings}
\usepackage{multicol}
\sisetup{output-decimal-marker = {,}, quotient-mode=fraction, output-exponent-marker=\ensuremath{\mathrm{3}}}
\end_preamble
\use_default_options true
\maintain_unincluded_children false
\language slovene
\language_package default
\inputencoding auto
\fontencoding global
\font_roman "default" "default"
\font_sans "default" "default"
\font_typewriter "default" "default"
\font_math "auto" "auto"
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\font_sc false
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\font_sf_scale 100 100
\font_tt_scale 100 100
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\bibtex_command default
\index_command default
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\spacing single
\use_hyperref false
\papersize default
\use_geometry true
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 1
\use_package esint 1
\use_package mathdots 1
\use_package mathtools 1
\use_package mhchem 1
\use_package stackrel 1
\use_package stmaryrd 1
\use_package undertilde 1
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification false
\use_refstyle 1
\use_minted 0
\index Index
\shortcut idx
\color #008000
\end_index
\leftmargin 1cm
\topmargin 0cm
\rightmargin 1cm
\bottommargin 2cm
\headheight 1cm
\headsep 1cm
\footskip 1cm
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
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\math_numbering_side default
\quotes_style german
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\paperpagestyle default
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header

\begin_body

\begin_layout Title
Osnovni izreki začetka analize
\end_layout

\begin_layout Author

\noun on
Anton Luka Šijanec
\end_layout

\begin_layout Date
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
today
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
newcommand
\backslash
euler{e}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{multicols}{2}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\frac{df}{dx}=f'(x_{0})=\lim_{h\to0}\frac{f(x_{0}+h)-f(x_{0})}{h}=\tan\varphi
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
(f(x)+g(x))'=f'(x)+g'(x)
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
(f(x)\cdot g(x))'=f'(x)\cdot g(x)+f(x)\cdot g'(x)
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
(c\cdot f(x))'=c\cdot f'(x)
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\left(\frac{f(x)}{g(x)}\right)'=\frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{g^{2}(x)}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
p\perp q\Rightarrow k_{p}=-k_{q}^{-1}\ ;\ \ \ p\parallel q\Rightarrow k_{p}=k_{q}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
(x^{r})'=r\cdot x^{r-1},x\in\mathbb{R}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\tan\varphi=\left|\frac{k_{2}-k_{1}}{1+k_{2}k_{1}}\right|
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
(g\circ f)'(x)=\left[g(f(x))\right]'=g(f(x))'\cdot f'(x)
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
(f^{-1}(x))'=\frac{-1}{f'(f^{-1}(x))}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\sin\alpha-\sin\beta=2\sin\frac{\alpha-\beta}{2}\cdot\cos\frac{\alpha+\beta}{2}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\lim_{x\to0}\frac{\sin x}{x}=1;\ \sin^{2}x+\cos^{2}x=1
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\sin'x=\cos x;\ \cos'x=-\sin x;\ \tan'x=\cos^{-2}x;\ \cot'x=-\sin^{-2}x
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
1+\tan^{2}x=\cos^{-2}x;\ 1+\cot^{2}x=\sin^{-2}x
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\arcsin'x=\frac{1}{\sqrt{1-x^{2}}}=-\arccos'x
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\arctan'x=\frac{1}{1+x^{2}}=-\text{arccot}'x
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\log_{a}(bc)=\log_{a}b+\log_{a}c;\ log_{a}b^{r}=r\cdot\log_{a}b;\ \log_{a}x=\frac{\log_{b}x}{\log_{b}a}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\log_{a}1=0
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
x>0\wedge a>0\Rightarrow\log_{1/a}x=-\log_{a}x
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
y=log_{a}x\Leftrightarrow x=a^{b};\ x=a^{\log_{a}x}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\lim_{\lvert t\rvert\to\infty}\left(1+t^{-1}\right)^{t}=\euler;\ t\ensuremath{\in\mathbb{R}}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\left(\log_{a}x\right)'=\frac{\log_{a}\euler}{x}=\frac{1}{x\cdot\ln a};\ \left(\ln x\right)'=x^{-1}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
(a^{x})'=a^{x}\ln a\Rightarrow(\euler^{x})'=\euler^{x}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
f(x_{0}+h)\approx f(x_{0})+f'(x_{0})\cdot h
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
x_{1,2}=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}
\]

\end_inset


\end_layout

\begin_layout Standard
Za možne napake ne odgovarjam.
 Srečno!
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
end{multicols}
\end_layout

\end_inset


\end_layout

\end_body
\end_document