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| author | Anton Luka Šijanec <anton@sijanec.eu> | 2023-04-11 23:08:30 +0200 |
|---|---|---|
| committer | Anton Luka Šijanec <anton@sijanec.eu> | 2023-04-11 23:08:30 +0200 |
| commit | f94086173cf17e9a1d6225b2a17b4e800a401838 (patch) | |
| tree | 7ec8ce17b8d5249048e478bd4e4cd6ff8e5f1081 /mat | |
| parent | merge(local, remote) (diff) | |
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Diffstat (limited to 'mat')
| -rw-r--r-- | mat/test/odvodi.lyx | 49 |
1 files changed, 44 insertions, 5 deletions
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 @@ -330,6 +341,28 @@ p\perp q\Rightarrow k_{p}=-k_{q}^{-1}\ ;\ \ \ p\parallel q\Rightarrow k_{p}=k_{q \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 +\[ y=log_{a}x\Leftrightarrow x=a^{b};\ x=a^{\log_{a}x} \] @@ -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 |