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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements
%%
# Drawing
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```
%%

File diff suppressed because it is too large Load Diff

View File

@@ -692,6 +692,9 @@ Pou
PzK
Pochodna
Pochodną
Przykłady
PJe
PStj
obj
oh
oq
@@ -1418,6 +1421,9 @@ ovN
oZf
oqn
oTa
ooo
oWiF
oRO
GoTo
GS
Gl
@@ -2080,6 +2086,8 @@ GIT
GfbfJfzf
GJFa
GUg
Głowa
GDb
Outline
ON
OD
@@ -2789,6 +2797,10 @@ OKF
Omó
OTy
OGB
ODH
OctK
ONVx
OOzU
endobj
endstream
ea
@@ -3496,6 +3508,10 @@ ewSC
eEE
eee
epGpwp
ego
eBkG
emx
emZ
Length
Link
LN
@@ -4174,6 +4190,7 @@ LAT
LeU
LIfBfr
Llq
LNP
Filter
FlateDecode
Font
@@ -4879,6 +4896,10 @@ Fzo
FDi
FbS
FjT
Fale
FlB
FFlm
FST
stream
sj
sR
@@ -5585,6 +5606,7 @@ sVP
sHr
skończona
severe
symbole
JQ
Js
JX
@@ -6232,6 +6254,14 @@ Jop
JQA
JfC
JkW
JeM
Jlya
JQu
JpL
JDu
JMmT
JQJ
JRLRFJ
xM
xw
xfkW
@@ -6951,6 +6981,7 @@ xNrq
xMDhW
xWe
xXoJ
xXW
QL
QW
QQx
@@ -7659,6 +7690,8 @@ QEU
QwZc
QTy
QNA
Qbjypir
Qgu
fVVhM
fW
fci
@@ -8299,6 +8332,7 @@ fDtD
fZQna
fLh
frac
fnvm
Bi
Border
Bh
@@ -9018,6 +9052,7 @@ BOHM
BJl
BoO
BwM
BPF
Trans
Type
TF
@@ -10408,6 +10443,9 @@ AyQ
AyR
AwpppXpDpTplpBpr
AhuJ
Adres
ANt
ACe
Subtype
SGw
SI
@@ -11783,6 +11821,9 @@ RlF
RFb
Równania
Rezystor
RyJT
RDxE
Rrt
Navigation
No
Nj
@@ -12445,6 +12486,10 @@ NrH
NKpZ
Nzmf
Nlu
Notacja
Nazwy
NhlE
NESCNH
ColorSpace
Contents
Cx
@@ -13126,6 +13171,10 @@ CEBE
CpH
Cewka
Ciągłość
Chomsky
CWP
CmAp
ChBD
ExtGState
Eu
EV
@@ -13853,6 +13902,9 @@ EMC
Ewqpq
EQEQTQ
Elementów
EIc
EIR
EEa
Xmo
XB
XK
@@ -14556,6 +14608,7 @@ XalJlF
XVg
XhKS
XkFD
XfR
VB
Vp
VE
@@ -15257,6 +15310,9 @@ VWR
VxN
VoR
VUY
VVWG
Voh
VJF
in
iy
ir
@@ -16006,6 +16062,9 @@ iKg
iHMH
int
istnieje
iIk
iXR
iNTF
vK
vE
vD
@@ -16697,6 +16756,9 @@ vFGT
vEmv
vfG
vklTl
vsXm
vXr
vwW
DXy
DB
Du
@@ -17391,6 +17453,8 @@ DQF
DbDrD
Date
Definicja
DFN
DRz
dA
dET
dg
@@ -18101,6 +18165,8 @@ drao
dNd
dNI
doy
doE
dcu
YI
YT
Yv
@@ -18777,6 +18843,8 @@ YTX
YbV
YTYZYQY
Yqf
YPD
YjK
cVuiT
cJ
cN
@@ -19496,6 +19564,9 @@ cZQ
cVy
circ
cdot
cXf
cdR
cVRm
bI
bx
bM
@@ -20209,6 +20280,8 @@ bpj
bkJe
bZm
bcbK
bajt
bOo
jW
je
jz
@@ -21569,6 +21642,15 @@ aVh
aEWX
ask
aYW
alfabet
abc
aaaabcccccc
aabbbc
abbccc
aaabbbccc
aZI
amTdF
aQK
uH
uS
uVn
@@ -22270,6 +22352,8 @@ umpmrmvmq
ubkW
uDW
ukT
uGLm
uML
Mh
MediaBox
MI
@@ -23012,6 +23096,10 @@ MIs
MEoqhqx
Meoyhyx
MTy
MHM
MRtf
Mtn
Mqg
lauG
lc
lS
@@ -23691,6 +23779,7 @@ lqD
lsv
lpX
lbwb
Kz
KM
Kw
@@ -24357,6 +24446,9 @@ KCHz
KzRz
KByy
Kondensator
KfC
KqI
KXb
IS
ID
IQT
@@ -25064,6 +25156,9 @@ IZW
Igz
IJAD
ISg
Inc
Ipp
IiO
qF
qIF
qy
@@ -25731,6 +25826,8 @@ qeu
qXo
qmuuj
qIn
qSVOXJ
qtq
Wd
WKo
Wm
@@ -26389,6 +26486,7 @@ WYU
WyXyRuW
WgU
WaoW
WtE
rM
ra
rv
@@ -27077,6 +27175,7 @@ rJl
rXcSBz
rHG
różniczkowalna
rJL
tI
tU
ta
@@ -27781,6 +27880,9 @@ tBjV
tyv
tEvE
tfL
terminalne
tLk
tbYua
wo
wHJ
wKe
@@ -28467,6 +28569,8 @@ wrt
wHb
wZt
warunkiem
wCx
wtM
pDJ
parenleftbigg
parenrightbigg
@@ -29205,6 +29309,9 @@ pgK
pVHW
punkcie
pain
pomocniczy
produkcji
pJYA
HD
Ho
Hg
@@ -29834,6 +29941,9 @@ Huw
HyN
HYx
HOim
HLo
HsW
HJw
UDq
Ue
UV
@@ -30513,6 +30623,11 @@ UwTo
UnE
UFe
Uqac
UbNM
UmV
Uxi
UAVBFG
UWM
yr
yukC
yF
@@ -31203,6 +31318,8 @@ ygzg
yeaYBV
yGg
yfu
yME
yDV
Zmo
ZS
ZW
@@ -31885,6 +32002,10 @@ ZuV
ZtH
ZAZ
ZpS
Zmg
ZZJ
ZsS
mD
ma
mj
@@ -32597,6 +32718,11 @@ mXG
mrR
mUg
mUE
metaalfabet
mtjh
mkk
mUQ
mUzE
nD
nF
nZ
@@ -33295,6 +33421,11 @@ nre
nwopovos
nuMlj
nlpu
nHagHX
njMI
noV
nMy
nKv
gNx
gHI
gri
@@ -33985,6 +34116,9 @@ gqZ
gVH
grp
granicę
gramatyki
gas
gQZ
kXk
kQ
kx
@@ -34676,6 +34810,10 @@ khzJ
kZaCaSasaK
kgf
krg
kDg
kQn
kOL
üx
ün
ür
@@ -35372,6 +35510,9 @@ hiZ
hhK
hIF
hIr
hDgF
hzb
hDz
zC
zZ
zZes
@@ -36080,6 +36221,10 @@ zgX
zgtd
zDfTfLf
zrzt
zmiennych
zfqd
znr
zOw
ÜI
Üj
ÜX
@@ -36221,6 +36366,7 @@ zrzt
Óz
ÓW
Óg
Ós
ęH
ęP
ęe

View File

@@ -1,9 +1,9 @@
{
"moveIntoMath_toggle": true,
"autoCloseMath_toggle": false,
"autoCloseRound_toggle": true,
"autoCloseSquare_toggle": true,
"autoCloseCurly_toggle": true,
"autoCloseRound_toggle": false,
"autoCloseSquare_toggle": false,
"autoCloseCurly_toggle": false,
"addAlignBlock_toggle": true,
"addAlignBlock_parameter": "align*",
"autoAlignSymbols": "= > < \\le \\ge \\neq \\approx",

View File

@@ -4,59 +4,22 @@
"type": "split",
"children": [
{
"id": "e3f67ff91e1a0ec7",
"id": "d78597a825f50ab5",
"type": "tabs",
"children": [
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"id": "2876d87cd78f8cc4",
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"type": "leaf",
"state": {
"type": "markdown",
"state": {
"file": "Elektrotechnika/Wykład/1 SEM/1 SEM.md",
"mode": "source",
"source": false
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}
},
{
"id": "9dfa8e90ce06f6bd",
"type": "leaf",
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"mode": "source",
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}
}
}
],
"currentTab": 3
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],
"direction": "vertical"
@@ -122,7 +85,7 @@
"state": {
"type": "backlink",
"state": {
"file": "AMiAL/Wykłady/1 SEM/20221125083233.md",
"file": "Myśli nieuczesane.md",
"collapseAll": false,
"extraContext": false,
"sortOrder": "alphabetical",
@@ -139,7 +102,7 @@
"state": {
"type": "outgoing-link",
"state": {
"file": "AMiAL/Wykłady/1 SEM/20221125083233.md",
"file": "Myśli nieuczesane.md",
"linksCollapsed": false,
"unlinkedCollapsed": true
}
@@ -162,7 +125,7 @@
"state": {
"type": "outline",
"state": {
"file": "AMiAL/Wykłady/1 SEM/20221125083233.md"
"file": "Myśli nieuczesane.md"
}
}
},
@@ -199,24 +162,24 @@
}
}
],
"currentTab": 4
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}
],
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View File

@@ -0,0 +1 @@
Jeżeli f jest różniczkowalna i $\Delta x \ne 0$ jest przyrostem $x$ to $dy=f'(x)\Delta x$ jest różniczką

View File

@@ -0,0 +1,26 @@
6)
$$\begin{align}
y &= \frac{2}{\sqrt[6]{x^{5}}}-\frac{x}{3}+\frac{\sqrt[4]{x^{3}}}{2}
\\
y &= \frac{2}{(x^{5})^{\frac{1}{6}}}-\frac{x}{3}+\frac{(x^3)^{\frac{1}{4}}}{2}
\\
y' &= 2(x^\frac{-11}{6})^{-\frac{5}{6}}-\frac{1}{3}+\frac{1}{2}*\frac{3}{4}*x^{-\frac{1}{4}}
\\
y' &= NaN
\end{align}$$
Można wyznaczyć pochodną tej funkcji za pomocą reguły różniczkowania złożonych funkcji. W szczególności, jeśli $f$ i $g$ są dwoma funkcjami, to pochodną funkcji $y=f(g(x))$ jest
$y' = f'(g(x)) \cdot g'(x)$
Możemy zastosować tę regułę do każdego składnika funkcji wyjściowej. W tym celu najpierw policzymy pochodne poszczególnych składników funkcji:
$\frac{dy}{dx} = \frac{dy}{dx} \left(\frac{2}{\sqrt[6]{x^{5}}}-\frac{x}{3}+\frac{\sqrt[4]{x^{3}}}{2}\right)$
$= \frac{dy}{dx} \left(\frac{2}{\sqrt[6]{x^{5}}}\right) - \frac{dy}{dx} \left(\frac{x}{3}\right) + \frac{dy}{dx} \left(\frac{\sqrt[4]{x^{3}}}{2}\right)$
$= \frac{1}{(\sqrt[6]{x^{5}})^2} \cdot \frac{dy}{dx} \left(\sqrt[6]{x^{5}}\right) - \frac{1}{3} \cdot \frac{dy}{dx}(x) + \frac{1}{4} \cdot \frac{dy}{dx} \left(\sqrt[4]{x^{3}}\right)$
$= \frac{1}{(\sqrt[6]{x^{5}})^2} \cdot \frac{dy}{dx} \left(\sqrt[6]{x^{5}}\right) - \frac{1}{3} \cdot 1 + \frac{1}{4} \cdot \frac{dy}{dx} \left(\sqrt[4]{x^{3}}\right)$

View File

@@ -0,0 +1,20 @@
![[20221209102007 2022-12-09 10.20.56.excalidraw]]
![[20221209102007 2022-12-09 10.37.42.excalidraw]]
![[20221209102007 2022-12-09 10.46.14.excalidraw]]
![[20221209102007 2022-12-09 10.56.09.excalidraw]]
![[20221209102007 2022-12-09 11.06.42.excalidraw]]
Rx=Rt Et/4Rt
Et
# 3

19
Myśli nieuczesane.md Normal file
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@@ -0,0 +1,19 @@
Co openAI ćpie:
To determine whether a sequence is monotonic, we must first determine whether the sequence is increasing or decreasing. To do this, we take the first derivative of the sequence and determine whether it is always positive, always negative, or has both positive and negative values.
For the given sequence $a_n=n^{2}-8n+15$, the first derivative is $a'_n=2n-8$. This expression is always negative for values of $n$ greater than 4, and always positive for values of $n$ less than 4. This means that the sequence is decreasing for values of $n$ greater than 4 and increasing for values of $n$ less than 4.
Therefore, the sequence is not monotonic because it is both increasing and decreasing. We can express this in LaTeX as follows:
$a_n=n^{2}-8n+15$ is not monotonic because its first derivative, $a'_n=2n-8$, has both positive and negative values.
The equation for adiabatic gas expansion is:
$$\frac{dU}{dt} = \frac{PdV}{dt}$$
where $U$ is the internal energy of the gas, $P$ is the pressure of the gas, and $V$ is the volume of the gas. This equation describes the change in the internal energy of the gas as it expands adiabatically, which means that there is no heat transfer between the gas and its surroundings.
$\mathbb{R}$

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@@ -0,0 +1,88 @@
```
date: 20221205115525
```
# Notacja Chomsky'ego:
$G=<V,\Sigma,P,\sigma>$, gdzie:
- V - symbole terminalne
- $\Sigma$ - metaalfabet - alfabet pomocniczy - symbole pomocnicze
- P - lista produkcji
- $\sigma$ - Głowa gramatyki
abc
aaaabcccccc
aabbbc
## $\begin{gathered}a^{n}b^{m}c^{k} &n,m,k\geqslant1\end{gathered}$
$G_{1}=<V_1,\Sigma_1,P_1,\sigma_1>$
$V_1 = \{a,b,c\}$
$\Sigma_1=\{\alpha,\beta,\gamma\}$
$P_1=\begin{cases}\alpha \rightarrow a\alpha \\ \alpha \rightarrow a\beta \\ \beta \rightarrow b\beta \\ \beta \rightarrow b\gamma \\ \gamma \rightarrow c\gamma \\ \gamma \rightarrow c \end{cases}$
$\sigma_1 = \alpha$
## $\begin{gathered}a^{n}b^{m}c^{n} &n,m\geqslant1\end{gathered}$
$G_{2}=<V_2,\Sigma_2,P_2,\sigma_2>$
$V_2 = \{a,b,c\}$
$\Sigma_2=\{\alpha,\beta\}$
$P_2=\begin{cases}\alpha \rightarrow a\alpha c \\ \alpha \rightarrow a\beta c \\ \beta \rightarrow b \beta \\ \beta \rightarrow b \end{cases}$
$\sigma_2 = \alpha$
## $\begin{gathered}a^{n}b^{n}c^{n} &n\geqslant 1 \end{gathered}$
$G_{3}=<V_2,\Sigma_2,P_2,\sigma_2>$
$V_3 = \{a,b,c\}$
$\Sigma_3=\{\alpha,\beta\}$
$P_3=\begin{cases}\alpha \rightarrow abc \\ \alpha \rightarrow a\alpha \beta c \\ b\beta \rightarrow bb \\ c\beta \rightarrow \beta c \end{cases}$
$\gamma = \alpha$
## Przykłady
abbccc w $G_1$
$\alpha \rightarrow^2 a\beta \rightarrow^3 ab\beta \rightarrow^4 abb\gamma \rightarrow^5 abbc\gamma \rightarrow^5 abbcc\gamma \rightarrow^6 abbccc$
Drzewo gramatyki
```
abbccc
||||||
|||||γ
||||γ
|||γ
||β
α
```
aaabbbccc $a^nb^nc^n$
$\alpha \rightarrow^2 a\alpha\beta c \rightarrow^2aa\alpha\beta c\beta c\rightarrow^1 aaabc\beta c\beta cc \rightarrow^{4,4} aaab\beta c\beta cc \rightarrow^4 aaab\beta\beta cc \rightarrow^3 aaabb\beta ccc\rightarrow^3 aaabbbccc$
# Notacja BNF:
$V={a,b,c}$
$\Sigma = \{<\alpha>,<\beta>\}$
$P = \begin{gathered}\{<\alpha>::= a<\alpha>c|a<\beta>c \\ <\beta>::= a \}\end{gathered}$
### Nazwy zmiennych:
$$\begin{gathered}
V=\{a..z,A..Z,0..9\} \\
\Sigma = \{<ident>,<litera>,<cyfra>\} \\
P=\{<ident>::=<litera>|<ident><litera>|<ident><cyfra>\\
<ident>::=a|..|z|A|..|Z \\
<cyfra>::=0|..|9 \} \\
\sigma = <ident>
\end{gathered}$$
### Adres IP
V={0..9,.}
Σ = {<IP>, <bajt>, <l1>,<l2>,<l3>, <0-9>
P={<IP>::=<bajt>.<bajt>.<bajt>.<bajt>
<bajt>::=<l1>|<l2>|<l3>
<l1>::=<0-9>
<0-9>::=0|<1-9>
<l2>::=<1-9><0-9>
<1-9>::=1|..|9
<l3>::=1<0-9><0-9>|2<0-4><0-9>|25<0-5>
<0-4>::=0|1|2|3|4
<0-5>::=5|<0-4>}
σ=<IP>