diff options
-rw-r--r-- | fiz/vaje/10/dokument.lyx | 1232 | ||||
-rw-r--r-- | mat/test/odvodi.lyx | 412 |
2 files changed, 412 insertions, 1232 deletions
diff --git a/fiz/vaje/10/dokument.lyx b/fiz/vaje/10/dokument.lyx deleted file mode 100644 index 3209653..0000000 --- a/fiz/vaje/10/dokument.lyx +++ /dev/null @@ -1,1232 +0,0 @@ -#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" -\font_default_family default -\use_non_tex_fonts false -\font_sc false -\font_osf false -\font_sf_scale 100 100 -\font_tt_scale 100 100 -\use_microtype false -\use_dash_ligatures true -\graphics default -\default_output_format default -\output_sync 0 -\bibtex_command default -\index_command default -\paperfontsize default -\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 2cm -\rightmargin 1cm -\bottommargin 2cm -\headheight 1cm -\headsep 1cm -\footskip 1cm -\secnumdepth 3 -\tocdepth 3 -\paragraph_separation indent -\paragraph_indentation default -\is_math_indent 0 -\math_numbering_side default -\quotes_style german -\dynamic_quotes 0 -\papercolumns 1 -\papersides 1 -\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 -Vsiljeno nihanje in resonanca -\end_layout - -\begin_layout Author - -\noun on -Anton Luka Šijanec -\end_layout - -\begin_layout Date -29. - marec 2023 -\end_layout - -\begin_layout Abstract -Grafi in rezultati desete in zadnje vaje pri predmetu -\noun on -F41 -\noun default - na Gimnaziji Bežigrad v 4. - letniku. -\end_layout - -\begin_layout Section* -Podatki in grafi -\end_layout - -\begin_layout Standard -Teoretični model -\begin_inset Formula $s_{0}\left(\nu\right)$ -\end_inset - - je -\begin_inset Formula -\[ -s_{0}=A\frac{\omega}{\sqrt{\left(\omega^{2}+\omega_{0}^{2}\right)^{2}+4\beta^{2}\omega^{2}}}\text{{,}} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -kjer je -\begin_inset Formula $\omega=2\pi v$ -\end_inset - - oziroma, če jo izračunamo iz podatkov matematičnega nihala, -\begin_inset Formula $\omega=\sqrt{\frac{g}{l}}$ -\end_inset - -. - Resonančna frekvenca, razbrana iz grafa — vrh, je -\begin_inset Formula $6,5$ -\end_inset - - radianov na sekundo, kar je -\begin_inset Formula $6,5\pi2$ -\end_inset - - nihajev na sekundo. -\end_layout - -\begin_layout Standard -\begin_inset Float table -placement H -wide false -sideways false -status open - -\begin_layout Plain Layout - -\lang english -\begin_inset Tabular -<lyxtabular version="3" rows="17" columns="4"> -<features tabularvalignment="middle"> -<column alignment="left" valignment="top" width="0pt"> -<column alignment="left" valignment="top" width="0pt"> -<column alignment="left" valignment="top" width="0pt"> -<column alignment="left" valignment="top" width="0pt"> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -\begin_inset Formula $l\left[\si{\meter}\right]$ -\end_inset - - -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $x_{0}\left[\si{\meter}\right]$ -\end_inset - - -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -\begin_inset Formula $\omega$ -\end_inset - - -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nu$ -\end_inset - - -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,4 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,012654 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -4,952272 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,788179 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,5 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,009038 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -4,429447 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,704968 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,45 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,009038 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -4,669047 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,743102 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,3 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,025308 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -5,718391 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,91011 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,35 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,019885 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -5,294202 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,842598 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,25 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,047 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -6,264184 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,996976 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,24 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,054231 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -6,393356 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -1,017534 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,23 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,054231 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -6,530863 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -1,039419 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,22 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,054231 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -6,677642 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -1,06278 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,21 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,056038 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -6,834785 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -1,08779 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,2 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,047 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -7,003571 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -1,114653 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,19 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,043385 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -7,185512 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -1,14361 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,18 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,043385 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -7,382412 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -1,174947 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,17 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,036154 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -7,596439 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -1,209011 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,16 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,032538 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -7,83023 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -1,24622 -\end_layout - -\end_inset -</cell> -</row> -<row> -<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,15 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -0,036154 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -8,087027 -\end_layout - -\end_inset -</cell> -<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> -\begin_inset Text - -\begin_layout Plain Layout - -\lang english -1,28709 -\end_layout - -\end_inset -</cell> -</row> -</lyxtabular> - -\end_inset - - -\end_layout - -\begin_layout Plain Layout -\align center -\begin_inset Caption Standard - -\begin_layout Plain Layout -Izmerjeni in izračunani podatki -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Float figure -placement H -wide false -sideways false -status open - -\begin_layout Plain Layout -\align center -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash -begin{tikzpicture} -\end_layout - -\begin_layout Plain Layout - - -\backslash -begin{axis}[width=0.75 -\backslash -textwidth, scale only axis, ylabel=$s_0$, domain=0:12, ytick pos=left, samples=2 -56, xlabel=$ -\backslash -omega$, xtick pos=bottom, xmin=0, xmax=12, ymin=0, ymax=.06, -\end_layout - -\begin_layout Plain Layout - -%grid=both -\end_layout - -\begin_layout Plain Layout - -, major grid style={dashed,blue}] -\end_layout - -\begin_layout Plain Layout - - -\backslash -addplot[only marks] table [x=omega, y=x, col sep=comma] {podatki.csv}; -\end_layout - -\begin_layout Plain Layout - - -\backslash -addlegendentry{meritve} -\end_layout - -\begin_layout Plain Layout - - -\backslash -addplot[blue] (x, {0.490752637*x/sqrt((x^2+6.6^2)^2+4*(-0.000179148908)^2*x^2)}); -\end_layout - -\begin_layout Plain Layout - - -\backslash -addlegendentry{Teoretični model} -\end_layout - -\begin_layout Plain Layout - -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addplot[mark=square*, blue, only marks] table [x=u, y=i, col sep=comma] - {2.csv}; -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addlegendentry{zaporedno} -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addplot[blue] (x, {x*1.1889}); -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addlegendentry{} -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addplot[mark=diamond*, green, only marks] table [x=u, y=i, col sep=comma] - {3.csv}; -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addlegendentry{vzporedno} -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addplot[blue] (x, {x*5.38536}); -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addlegendentry{} -\end_layout - -\begin_layout Plain Layout - - -\backslash -end{axis} -\end_layout - -\begin_layout Plain Layout - -% -\backslash -begin{axis}[width=0.75 -\backslash -textwidth, scale only axis, ylabel=$b^{-1}$, ytick pos=right, samples=256, - xlabel=$a^{-1}$, xtick pos=top, %grid=both -\end_layout - -\begin_layout Plain Layout - -%, xlabel near ticks, ylabel near ticks, major grid style={dashed,red}, -\end_layout - -\begin_layout Plain Layout - -%legend style={at={(0.975,0.325)}, anchor=south east}, domain=4:7, xmin=4, - xmax=6.6, ymin=13, ymax=15.6 -\end_layout - -\begin_layout Plain Layout - -%] -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addplot[mark=triangle*, red, only marks] table [x=1/a, y=1/b, col sep=comma] - {podatki.csv}; -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addlegendentry{meritve} -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addplot[red] (x, {1/0.0511438-x}); -\end_layout - -\begin_layout Plain Layout - -% -\backslash -addlegendentry{$b^{-1}=f^{-1}-a^{-1}$} -\end_layout - -\begin_layout Plain Layout - -% -\backslash -end{axis} -\end_layout - -\begin_layout Plain Layout - - -\backslash -end{tikzpicture} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Plain Layout -\begin_inset Caption Standard - -\begin_layout Plain Layout -\begin_inset CommandInset label -LatexCommand label -name "fig:graf-1" - -\end_inset - - -\begin_inset Formula $s_{0}\left(\omega\right)$ -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Meritve se ne ujemajo z napovedano vrednostjo. -\end_layout - -\end_body -\end_document diff --git a/mat/test/odvodi.lyx b/mat/test/odvodi.lyx new file mode 100644 index 0000000..01a1908 --- /dev/null +++ b/mat/test/odvodi.lyx @@ -0,0 +1,412 @@ +#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" +\font_default_family default +\use_non_tex_fonts false +\font_sc false +\font_osf false +\font_sf_scale 100 100 +\font_tt_scale 100 100 +\use_microtype false +\use_dash_ligatures true +\graphics default +\default_output_format default +\output_sync 0 +\bibtex_command default +\index_command default +\paperfontsize default +\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 +\is_math_indent 0 +\math_numbering_side default +\quotes_style german +\dynamic_quotes 0 +\papercolumns 1 +\papersides 1 +\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 +\[ +\tan\varphi=\lvert\frac{k_{2}-k_{1}}{1+k_{2}k_{1}}\rvert +\] + +\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 +\[ +\arcsin'x=\frac{1}{\sqrt{1-x^{2}}}=-\arccos'x;\ \arctan'x=\frac{1}{1+x^{2}}=-\text{arccot}'x +\] + +\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 +\[ +y=log_{a}x\Leftrightarrow x=a^{b};\ x=a^{\log_{a}x} +\] + +\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 + +\end_layout + +\begin_layout Standard +Za možne napake ne odgovarjam. + Vse te izreke najdemo v učbeniku. + 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 |