From f94086173cf17e9a1d6225b2a17b4e800a401838 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= <anton@sijanec.eu>
Date: Tue, 11 Apr 2023 23:08:30 +0200
Subject: zgo zadnji test (upam)

---
 mat/test/odvodi.lyx | 49 ++++++++++++++++++++++++++++++++++++++++++++-----
 1 file changed, 44 insertions(+), 5 deletions(-)

(limited to 'mat')

diff --git a/mat/test/odvodi.lyx b/mat/test/odvodi.lyx
index 01a1908..e2f11dc 100644
--- a/mat/test/odvodi.lyx
+++ b/mat/test/odvodi.lyx
@@ -231,7 +231,7 @@ p\perp q\Rightarrow k_{p}=-k_{q}^{-1}\ ;\ \ \ p\parallel q\Rightarrow k_{p}=k_{q
 \begin_layout Standard
 \begin_inset Formula 
 \[
-\tan\varphi=\lvert\frac{k_{2}-k_{1}}{1+k_{2}k_{1}}\rvert
+\tan\varphi=\left|\frac{k_{2}-k_{1}}{1+k_{2}k_{1}}\right|
 \]
 
 \end_inset
@@ -286,7 +286,7 @@ p\perp q\Rightarrow k_{p}=-k_{q}^{-1}\ ;\ \ \ p\parallel q\Rightarrow k_{p}=k_{q
 \begin_layout Standard
 \begin_inset Formula 
 \[
-\sin'x=\cos'x;\ cos'x=-\sin x;\ \tan'x=\cos^{-2}x;\ \cot'x=-\sin^{-2}x
+\sin'x=\cos x;\ \cos'x=-\sin x;\ \tan'x=\cos^{-2}x;\ \cot'x=-\sin^{-2}x
 \]
 
 \end_inset
@@ -297,7 +297,7 @@ p\perp q\Rightarrow k_{p}=-k_{q}^{-1}\ ;\ \ \ p\parallel q\Rightarrow k_{p}=k_{q
 \begin_layout Standard
 \begin_inset Formula 
 \[
-1+\tan^{2}x=cos^{-2}x;\ 1+\cot^{2}x=\sin^{-2}x
+1+\tan^{2}x=\cos^{-2}x;\ 1+\cot^{2}x=\sin^{-2}x
 \]
 
 \end_inset
@@ -308,7 +308,18 @@ p\perp q\Rightarrow k_{p}=-k_{q}^{-1}\ ;\ \ \ p\parallel q\Rightarrow k_{p}=k_{q
 \begin_layout Standard
 \begin_inset Formula 
 \[
-\arcsin'x=\frac{1}{\sqrt{1-x^{2}}}=-\arccos'x;\ \arctan'x=\frac{1}{1+x^{2}}=-\text{arccot}'x
+\arcsin'x=\frac{1}{\sqrt{1-x^{2}}}=-\arccos'x
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\arctan'x=\frac{1}{1+x^{2}}=-\text{arccot}'x
 \]
 
 \end_inset
@@ -325,6 +336,28 @@ 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 
+\[
+\log_{a}1=0
+\]
+
+\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
@@ -383,12 +416,18 @@ f(x_{0}+h)\approx f(x_{0})+f'(x_{0})\cdot h
 \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.
- Vse te izreke najdemo v učbeniku.
  Srečno!
 \end_layout
 
-- 
cgit v1.2.3