From 4b585ac13440e7a5bd7a5bc4dceb304c3c471bff Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= Date: Thu, 6 Apr 2023 22:21:05 +0200 Subject: mat zadnji test, upam --- fiz/vaje/10/dokument.lyx | 1232 ---------------------------------------------- mat/test/odvodi.lyx | 412 ++++++++++++++++ 2 files changed, 412 insertions(+), 1232 deletions(-) delete mode 100644 fiz/vaje/10/dokument.lyx create mode 100644 mat/test/odvodi.lyx 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. 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-\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 - 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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 -- cgit v1.2.3