From 6b729e759e81d6978e66c16e89118e9663c094c7 Mon Sep 17 00:00:00 2001 From: VectorKappa Date: Sun, 19 Feb 2023 20:44:26 +0100 Subject: [PATCH] vault backup: 2023-02-19 20:44:45 --- .obsidian/appearance.json | 2 +- .../obsidian-completr/scanned_words.txt | 191 ++++++++++++++++++ .obsidian/workspace.json | 44 ++-- AMiAL/!Materiały/poch_zast.pdf | Bin 0 -> 173642 bytes AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 1.md | 46 ++++- AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 2.md | 19 ++ .../Ćwiczenia/Zadania/Różniczki/Zadanie 1.md | 46 +++++ 7 files changed, 320 insertions(+), 28 deletions(-) create mode 100644 AMiAL/!Materiały/poch_zast.pdf create mode 100644 AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 2.md create mode 100644 AMiAL/Ćwiczenia/Zadania/Różniczki/Zadanie 1.md diff --git a/.obsidian/appearance.json b/.obsidian/appearance.json index 5ca226e..3b3fd0a 100644 --- a/.obsidian/appearance.json +++ b/.obsidian/appearance.json @@ -5,5 +5,5 @@ "textFontFamily": "Lexend Deca", "monospaceFontFamily": "SauceCodePro Nerd Font Mono", "accentColor": "#ef6b6b", - "baseFontSize": 20 + "baseFontSize": 15 } \ No newline at end of file diff --git a/.obsidian/plugins/obsidian-completr/scanned_words.txt b/.obsidian/plugins/obsidian-completr/scanned_words.txt index 0108759..c32f655 100644 --- a/.obsidian/plugins/obsidian-completr/scanned_words.txt +++ b/.obsidian/plugins/obsidian-completr/scanned_words.txt @@ -1325,6 +1325,12 @@ PSd PSK PWR PRXIHZ +POY +PHX +PeD +PIsq +PEus +POO obj oh oq @@ -2649,6 +2655,9 @@ oTS oSC otf obliczyć +oTO +oUer +oHB GoTo GS Gl @@ -3895,6 +3904,13 @@ GrI GXX GPr Gnvr +GJI +GiCL +GDwF +GbP +GlR +GkL +GWZ Outline ON OD @@ -5202,6 +5218,11 @@ Obliczanie OTG OQpd OTBXXV +ODvX +OzJxcS +OhY +Oiy +Opisać endobj endstream ea @@ -6553,6 +6574,11 @@ ekstrema eLk esx epA +eun +eoN +eHK +euv +eyp Length Link LN @@ -7841,6 +7867,12 @@ Ltt LvH LnP LrX +LMWp +Lue +Lkd +LYs +LpL +LOKNCA Filter FlateDecode Font @@ -9160,6 +9192,11 @@ FOC FBC FWBTFN FJHFSK +FeI +FfsE +FEo +FtTV +Fplu stream sj sR @@ -10494,6 +10531,9 @@ styczna sxi sSi ssp +sKe +suIw +sSs JQ Js JX @@ -11764,6 +11804,9 @@ JBeq Jjt JNX JYeb +JxL +JwV +JpJ xM xw xfkW @@ -13079,6 +13122,9 @@ xkv xBl xGn xit +xPs +xsN +xsG QL QW QQx @@ -14384,6 +14430,10 @@ QQUUDTEUET QAG QzR QnL +QRU +QCk +QMOa +QkWB fVVhM fW fci @@ -15704,6 +15754,10 @@ fAo feWl fjT fNI +fuMP +fyV +fpRFL +fVoef Bi Border Bh @@ -17040,6 +17094,9 @@ BXqi BnVl BHh BDi +BWU +BIHMDV +BYSYRX Trans Type TF @@ -18407,6 +18464,7 @@ TVDiA TFv TiQ TJNLRR +TJS Annots Annot Aac @@ -19681,6 +19739,9 @@ ALjTJ AzYh Aoh AVTtc +Aoy +AoY +AUETFF Subtype SGw SI @@ -20978,6 +21039,9 @@ SLII SQV SKS SWB +Sbg +SlW +SNiF Rect Re Resources @@ -22275,6 +22339,11 @@ RRxo Ruf RTb RUIYCL +RvtI +Rva +RUR +RVM +RŁ Navigation No Nj @@ -23566,6 +23635,9 @@ NYm NCpw NNO NyF +Nzc +NrX +NHw ColorSpace Contents Cx @@ -24885,6 +24957,10 @@ ChV CxAxQx CIE CFB +CzU +CJUE +Cwww +CUk ExtGState Eu EV @@ -27489,6 +27565,8 @@ Xkn XYG XOv XqM +XDj +XPc VB Vp VE @@ -28810,6 +28888,9 @@ VaXX VOy VgS VkXG +Vlru +Vxf +VGoG in iy ir @@ -30175,6 +30256,9 @@ iiLH iIf iSc iDs +itF +iSH +iuxy vK vE vD @@ -31484,6 +31568,9 @@ vKX vwu vDd vdR +vfu +vlp +vWpi DXy DB Du @@ -32753,6 +32840,9 @@ DTU DuT DJi DuL +DYHMTS +Dqe +DnI dA dET dg @@ -34102,6 +34192,8 @@ dSGz dUVQ dVn definicji +dpp +dziedziny YI YT Yv @@ -35424,6 +35516,12 @@ Yxv YJI YcK YSX +YLuR +YGql +YFI +Ymu +YmS +Yek cVuiT cJ cN @@ -36734,6 +36832,11 @@ cXK clI cTemFa cZl +cJL +cae +cWV +ciT +cDM bI bx bM @@ -38083,6 +38186,11 @@ bPc blL bEbs boo +btF +bgV +bVF +bzT +brFxw jW je jz @@ -40661,6 +40769,10 @@ aCAU aGsF aZeK ayZi +aYAL +aexdI +aOe +analitycznie uH uS uVn @@ -41956,6 +42068,9 @@ uQi umw ulW uBP +uIv +uiT +układzie Mh MediaBox MI @@ -43295,6 +43410,11 @@ Monotoniczność MaO MMUHGV MPx +MDe +MDJgC +MMy +MUiB +MbA lauG lc lS @@ -44578,6 +44698,11 @@ lqj llVa lwYb lOF +lov +lYw +lLoP +lfB +lts Kz KM Kw @@ -45846,6 +45971,8 @@ KNe KrqxZ Kvm KHn +KWE +Korzystając IS ID IQT @@ -47164,6 +47291,10 @@ IRu IuV IIh IGDAFA +ITG +IVsy +IsZfc +IBd qF qIF qy @@ -48442,6 +48573,8 @@ qpz qoDzs qVB qNI +qYvO +qnI Wd WKo Wm @@ -49726,6 +49859,7 @@ WWW Wtg WHz WKi +WQWSCF rM ra rv @@ -51065,6 +51199,10 @@ rvT rGQu różniczką rms +rHW +rdv +rrKJ +różniczki tI tU ta @@ -52378,6 +52516,7 @@ tYg tbfU tpL twK +twJw wo wHJ wKe @@ -53628,6 +53767,13 @@ wvs wlM wäIl wEHP +wEL +wOz +wMN +wRy +wartość +wyrażenia +współrzędnych pDJ parenleftbigg parenrightbigg @@ -54975,6 +55121,10 @@ pok podstawie pochodną podanym +pZwp +pYOz +przybliżoną +pochodne HD Ho Hg @@ -56201,6 +56351,11 @@ HWke HZm Hpc Hmlz +HHti +HHw +HltII +HGP +HRPJKT UDq Ue UV @@ -57519,6 +57674,12 @@ UEL Uzb UmF UINDEK +UxU +UMzC +UTXLOY +Uzt +UFO +UUe yr yukC yF @@ -58799,6 +58960,7 @@ ydm ymeP ygU ydf +yole Zmo ZS ZW @@ -60116,6 +60278,11 @@ ZwX ZwOb ZWt ZVz +ZYR +ZTJ +ZQQH +Zan +ZcRA mD ma mj @@ -61443,6 +61610,8 @@ mmT mkh mdw mDn +mGv +mlxG nD nF nZ @@ -62740,6 +62909,10 @@ normalna nYd niE nMnz +nucg +nTk +neub +naszkicować gNx gHI gri @@ -64050,6 +64223,7 @@ gwS granic gUQ gxV +gfBb kXk kQ kx @@ -65403,6 +65577,11 @@ kqC kNF kIx ksd +kQw +kXl +kBe +kTXMj +kLA üx ün ür @@ -66750,6 +66929,13 @@ hä hVE hhJRFTWEV hNu +hBz +hct +hGn +hAra +hku +hQQr +hbE zC zZ zZes @@ -68056,6 +68242,9 @@ zkv zQY zpf zhoK +zqvj +zeG +zuAg ÜI Üj ÜX @@ -68137,6 +68326,7 @@ zhoK Żd ŻP ŻU +ŻJ ńE ńk ńq @@ -68360,6 +68550,7 @@ zhoK ęE ęJ ęj +ęc śy środku śq diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 0296072..df784fd 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -8,38 +8,37 @@ "type": "tabs", "children": [ { - "id": "b7ecae67f8974f5b", + "id": "81d0b2145326025c", "type": "leaf", "state": { "type": "markdown", "state": { - "file": "Elektrotechnika/Ćwiczenia/20221209102007.md", + "file": "AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 2.md", "mode": "source", "source": false } } }, { - "id": "ad833fdc986b00e4", + "id": "ecc53cb8ed19425a", "type": "leaf", "state": { "type": "markdown", "state": { - "file": "AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 1.md", + "file": "AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 2.md", "mode": "source", "source": false } } } - ], - "currentTab": 1 + ] }, { - "id": "14235bb2932012f6", + "id": "17a276c831896291", "type": "tabs", "children": [ { - "id": "f24465f327c9d7d7", + "id": "0e6931af2058a8c6", "type": "leaf", "state": { "type": "pdf", @@ -114,7 +113,7 @@ "state": { "type": "backlink", "state": { - "file": "AMiAL/!Materiały/pochodna.pdf", + "file": "AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 2.md", "collapseAll": false, "extraContext": false, "sortOrder": "alphabetical", @@ -131,7 +130,7 @@ "state": { "type": "outgoing-link", "state": { - "file": "AMiAL/!Materiały/pochodna.pdf", + "file": "AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 2.md", "linksCollapsed": false, "unlinkedCollapsed": true } @@ -154,7 +153,7 @@ "state": { "type": "outline", "state": { - "file": "AMiAL/!Materiały/pochodna.pdf" + "file": "AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 2.md" } } }, @@ -195,7 +194,8 @@ } ], "direction": "horizontal", - "width": 300 + "width": 300, + "collapsed": true }, "left-ribbon": { "hiddenItems": { @@ -212,17 +212,17 @@ "breadcrumbs:Breadcrumbs Visualisation": false } }, - "active": "a7fe127a169a5f82", + "active": "81d0b2145326025c", "lastOpenFiles": [ + "AMiAL/Ćwiczenia/Zadania/Różniczki/Zadanie 1.md", + "AMiAL/Ćwiczenia/1 SEM/20221014121234.md", + "AMiAL/Ćwiczenia/Zadania/Całki/1.md", + "AMiAL/Ćwiczenia/Zadania/ciagi_gr/Zadanie 1.md", + "AMiAL/Ćwiczenia/Zadania/funkcje/Zadanie 1.md", + "AMiAL/Ćwiczenia/Zadania/funkcje/Zadanie 2.md", + "AMiAL/Ćwiczenia/Zadania/li_zesp/Zadanie 1.md", "AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 1.md", - "AMiAL/!Materiały/pochodna.pdf", - "Elektrotechnika/Ćwiczenia/20221209102007.md", - "Elektrotechnika/Ćwiczenia/20221125102535.md", - "Elektrotechnika/Ćwiczenia/20221123102116.md", - "Elektrotechnika/Ćwiczenia/20221028102800.md", - 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$f(x)=3+2\sqrt{4x-1},\ x_{0}=2\frac{1}{2}$ -$f'(x)=\frac{2}{2\sqrt{4x-1}}$ -$f'(x_{0})=\frac{1}{2}$ +$f'(x)=2\cdot \frac{1}{2\sqrt{4x-1}}\cdot 4$ +$f'(x_{0})=\frac{4}{3}$ +## 8 +$f(x)=\frac{1}{x^{2}},\ x_{0}=1$ +$f'(x)=-\frac{2}{x^3}$ +$f'(x_{0})=-2$ +## 9 +$f(x)=\frac{2}{x^{3}},\ x_{0}=-1$ +$f(x)=2(x^{-3})$ +$f'(x)=-\frac{6}{x^{4}}$ +$f'(x_{0})=-6$ +## 10 +$f(x)=\sqrt{x^{2}-1},\ x_{0}=-3$ +$f'(x)=\cfrac{1}{2\sqrt{x^{2}-1}} \cdot 2x$ +$f'(x_{0})=\frac{-6}{4\sqrt{2}}=\frac{-3}{2\sqrt{2}}$ +## 11 +$f(x)=\sqrt{2x^{2}+1},\ x_{0}=2$ +$f'(x)=\cfrac{1}{2\sqrt{2x^{2}+1}} \cdot 4x$ +$f'(x_{0})=\frac{4}{3}$ +## 12 +$f(x)=\sin{x},\ x_{0}=\frac{\pi}{2}$ +$f'(x)=\cos x$ +$f'(x_{0})=0$ +## 13 +$f(x)=\cos{x},\ x_{0}=\frac{\pi}{2}$ +$f'(x)=-\sin x$ +$f'(x_{0})=-1$ +## 14 +$f(x)=\sin{x^2},\ x_{0}=0$ +$f'(x)=\cos x^{2}\cdot 2x$ +$f'(x_{0})=0$ +## 15 +$f(x)=\sin\sqrt{x},\ x_{0}=0$ +$f'(x)=\cos\sqrt{x}\cdot\frac{1}{2\sqrt{x}}$ +$f'(x_{0})=1\cdot\frac{1}{0}=brak\ rozwiązania$ + + diff --git a/AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 2.md b/AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 2.md new file mode 100644 index 0000000..699fdf1 --- /dev/null +++ b/AMiAL/Ćwiczenia/Zadania/Pochodne/Zadanie 2.md @@ -0,0 +1,19 @@ +# Wyznaczyć pochodne podanych funkcji. +## 1 +$y=(3-x^{4})^{2}$ +$y'=2(3-x^{4})\cdot(-4x^{3})=(6-2x^{4})\cdot(-4x^{3})=-24x^{3}+8x^{7}$ +## 2 +$y=1-\frac{4}{x^6}+\frac{3}{x^7}$ +$y'=-4\cdot-6x^{-7}+3\cdot-7x^{-8}=\frac{24}{x^{7}}-\frac{21}{x^{8}}$ +## 3 +$y=\cfrac{x^{2}+4}{x}$ +$y'=\cfrac{1}{x^{2}}\cdot\left(2x^{2}-(x^{2}+4)\right)=\cfrac{x^{2}-4}{x^{2}}=1-\cfrac{4}{x^2}$ +## 4 +$y=\cfrac{x-3}{x^{2}}$ +$y'=\cfrac{1}{x^{4}}\cdot\left(x^{2}-2x^{2}+6x\right)=\cfrac{6x-x^{2}}{x^{4}}=\cfrac{6-x}{x^3}$ +## 5 +$y$ +## 7 +$y=\cfrac{x^{5}+x^{3}+x}{\sqrt{x}}$ +$y'=\cfrac{1}{x}\left((x^{5}+x^{3}+x)\cdot\frac{1}{2\sqrt{x}}-(5x^{4}+3x^2+1)\cdot\sqrt{x}\right)$ + diff --git a/AMiAL/Ćwiczenia/Zadania/Różniczki/Zadanie 1.md b/AMiAL/Ćwiczenia/Zadania/Różniczki/Zadanie 1.md new file mode 100644 index 0000000..e813ee2 --- /dev/null +++ b/AMiAL/Ćwiczenia/Zadania/Różniczki/Zadanie 1.md @@ -0,0 +1,46 @@ +# Korzystając z różniczki wyznaczyć przybliżoną wartość wyrażenia. +## 1 +$\sqrt{2.01^{4}+9}=\left.5+df\right|_{(x_{0})}$ +$x_0=2$ +$\Delta x = 0.01$ +$f(x)=\sqrt{x^4+9}$ +$f'(x)=\frac{1}{2\sqrt{x^{4}+9}}\cdot4x^{3}$ +$f'(x_{0})=3.2$ +$\left.df\right|_{x_{0}}=3.2\cdot0.01=0.032$ +$\sqrt{2.01^{4}+9}\approx5.032$ +## 2 +$(0.98^{2}+2)^3=27+\left.df\right|_{(x_{0})}$ +$x_{0}=1$ +$\Delta x=-0.02$ +$f(x)=(x^{2}+2)^3$ +$f'(x)=3(x^{2}+2)^{2}\cdot2x$ +$f'(x_{0})=54$ +$\left.df\right|_{x_{0}}=54\cdot(-0.02)=-1.08$ +$(0.98^{2}+2)^{3}=27+(-1.08)=25.92$ +## 3 +$\cfrac{4\cdot2.03+1}{2.03^{2}-2}=\frac{9}{2}+\left.df\right|_{(x_{0})}$ +$x_{0}=2$ +$\Updelta x=0.03$ +$f(x)=\cfrac{4x+1}{x^{2}-2}$ +$f'(x)=\cfrac{1}{\left(x^{2}-2\right)^{2}}\cdot\left(4\cdot(x^{2}-2)-(4x+1)\cdot2x\right)$ +$f'(x_{0})=-\cfrac{28}{4}=-7$ +$\left.df\right|_{(x_{0})}=-7\cdot0.03=-0.21$ +$\cfrac{4\cdot2.03+1}{2.03^{2}-2}=4.5+(-0.21)=4.29$ +## 4 +$\ln(1+\ln 1.01)=0+\left.df\right|_{x_{0}}$ +$f(x)=\ln(1+\ln x)$ +$x_{0}=1$ +$\Delta x=0.01$ +$f'(x)=\cfrac{1}{1+\ln x}\cdot\cfrac{1}{x}$ +$f'(x_{0})=1$ +$\left.df\right|_{x_{0}}=0.01$ +$\ln(1+\ln 1.01)=0+0.01=0.01$ +## 5 +$0.99\cdot\cos(0.99\pi)=-1+\left.df\right|_{x_{0}}$ +$f(x)=x\cdot\cos(x\pi)$ +$x_0=1$ +$\Delta x = -0.01$ +$f'(x)=cos(x\pi)+x\cdot(-\sin(\pi x)\cdot\pi)$ +$f'(x_{0})=\cos(\pi)-\pi(\sin\pi)=-1$ +$\left.df\right|_{x_{0}}=-1\cdot(-0.01)=0.01$ +$0.99\cdot\cos(0.99\pi)=-0.99$ \ No newline at end of file