prokop/zpevnik
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

calculus rhapsody final

Browse Source 
dokonceni zpevniku, logo z MA1 skript
This commit is contained in:
prokop
2026-07-20 21:24:00 +02:00
parent 3c4da098c3
commit 202cab5091
6 changed files with 833 additions and 47 deletions
Download Patch File Download Diff File Expand all files Collapse all files
pisne/calculusRhapsody.tex
+39 -42
View File
@@ -2,76 +2,73 @@
\begin{verse}
^{G7}Is this $x$ defined? ^{C7}Is $f$ ^*{Gm7}con ^*{C7}ti ^*{Gm7}nu ^{C7}ous? \\
^{F7}How do you ^{Cm7}find ^{F7}out? You can ^{B}use the ^*{Cm7} li^{B}mit ^*{F7} pro^{B}cess. \\
^{Gm7}Approach from both sides, The ^{B7}left and the right and ^{Eb}meet. \\
^{Gm7}Approach from both sides, the ^{B7}left and the right and ^{Eb}meet. \\
^{Cm7}I'm a just a limit, ^{F7}defined analytically. Functions \\
^*{H}continu ^{B}ous, ^{A}Theres no ^{B}holes, ^{H}No sharp ^{B}points, ^{A}Or asymp^{B}totes. \\
^*{H}continu ^{B}ous, ^{A}Theres no ^{B}holes, ^{H}No sharp ^{B}points, ^{A}or asymp^{B}totes. \\
^{Eb}Any way this ^{B}graph goes. ^{C#dim7}It is diffe^{F7}rentiable for me for ^{B}me.
\end{verse}
\begin{verse}
^{B}All year, in ^{Gm}Calculus Weve ^{Cm}learned so many things \\
About which ^{Cm7}we are going to ^{F7}sing \\
^{B}We can find derivatives And ^{Gm}integrals \\
^{B}All year, in ^{Gm}Calculus. We've ^{Cm}learned so many things. \\
About which ^{Cm7}we are going to ^{F7}sing. \\
^{B}We can find derivatives and ^{Gm}integrals. \\
And ^{Cm}the area en^{Eb}closed bet^{Eb}ween ^{Am7}two curves.
\end{verse}
\begin{verse}
^{Eb}$y$ prime ^{H}oooh^{Cm}\_\_\_ Is the ^{Fm}derivative ^{E5+}of ^{Ab}$y$ \\
^{Eb}$y$ prime ^{H}oooh^{Cm}\_\_\_. Is the ^{Fm}derivative ^{E5+}of ^{Ab}$y$ \\
$y$ ^{B7}equals $x$ to the $n$, $dy/dx$ \\
^{B}Equals ^{Cm}$n$ times ^{Abm}$x$ To the ^{Eb}$n-1$. \\
\end{verse}
\begin{verse}
^{B}Other a^{Gm}pplications Of de^{Cm}rivatives apply \\
^{B}Other a^{Gm}pplications of de^{Cm}rivatives apply \\
If $y$ is di^{Cm7}vided or multi^{F7}plied \\
^{B}You use the quotient And ^{Gm}product rules \\
And ^{Cm}dont you for^{Eb}get To ^{B}do ^{Ab}the dance ^{Eb} \\
^{B}You use the quotient and ^{Gm}product rules \\
and ^{Cm}dont you for^{Eb}get To ^{B}do ^{Ab}the dance ^{Eb} \\
\end{verse}
\begin{verse}
^{Eb}Also ^{B}oooh^{Cm}\_\_\_ (dont forget the chain rule) \\
^{Fm}Before you are ^*{Ab}done ^{Dm7}, You ^{B7}gotta remember to multiply by the chain \\
^{Fm}before you are ^*{Ab}done ^{Dm7}, You ^{B7}gotta remember to multiply by the chain. \\
\end{verse}
Mezihra, crazy kytarové sólo
\begin{verse}
^{A} ^{D}I ^{A}need to ^{Adim}find ^{A}the ^{D}area ^{A}under a ^{Adim}curve \\
^*{A}Inte ^{D}grate! ^*{A}Inte ^{D}grate! ^{A}You can ^{Adim}use the ^*{A}inte ^*{D}gra ^{A}tion \\
^{Db}Raise exponent ^{Ab7}by one ^{C}multiply the ^*{E7}recipro ^{A}cal \\
Add a constant Add a constant \\
Add a constant Add a constant \\
Add a constant labeled $C$ \\
^{A} ^{D}I ^{A}need to ^{Adim}find ^{A}the ^{D}area ^{A}under a ^{Adim}curve. \\
^*{A}Inte ^{D}grate! ^*{A}Inte ^{D}grate! ^{A}You can ^{Adim}use the ^*{A}inte ^*{D}gra ^{A}tion. \\
^{Db}Raise exponent ^{Ab7}by one ^{C}multiply the ^*{E7}recipro ^{A}cal. \\
Add a constant Add a constant! \\
Add a constant Add a constant! \\
Add a constant labeled $C$. \\
(Labeled $C$-ee-ee-ee-ee) \\
\end{verse}
\begin{verse}
^{H}Im ^{B}just a ^*{A}cons ^{B}tant ^*{H}No ^{B}body ^{A}loves ^{B}me. \\
^{Ab}He's ^{Eb}just a ^*{Ebdim}cons ^{Eb}tant ^{Ab}Might as ^{Eb}well just ^{Ebdim}call it ^{Eb}$C$ \\
^{Ab}Never for^{Eb}get to add ^{F7}the constant ^{B}$C$ \\
^{H}I'm ^{B}just a ^*{A}cons ^{B}tant ^*{H}no ^{B}body ^{A}loves ^{B}me. \\
^{Ab}He's ^{Eb}just a ^*{Ebdim}cons ^{Eb}tant ^{Ab}might as ^{Eb}well just ^{Ebdim}call it ^{Eb}$C$. \\
^{Ab}Never for^{Eb}get to add ^{F7}the constant ^{B}$C$. \\
\end{verse}
\begin{verse}
Can you find the area between $f$ and $g$ \\
In-te-grate $f$ and then integrate $g$ \\
(then subtract) \\
To revolve around the y-axis \\
(integrate) \\
outer radius squared minus inner radius squared \\
(multiplied) \\
multiplied by $\pi$ \\
(multiply) \\
Multiply the integral by $\pi$! \\
$\pi$ tastes real good with whipped cream! \\
Mama-Mia, Mama-Mia \\
Mama-Mia let me go. \\
Pre-calculus did not help me to prepare for Calculus, for Calculus, help me! \\
^{H}Can you ^{B}find ^{A}the ^{B}area ^{H}between ^{B}$f$ and ^{A}$g$ \\
^*{B}In- ^*{Eb}te- ^{B}grate ^{Eb}$f$ ^{B}and then ^*{Eb}in ^*{B7}te ^{Eb}grate ^{B}$g$. ^{Eb}(then subtract) \\
To revolve ^{Eb}around the y-axis (integrate) \\
outer radius squared minus inner radius squared (multiplied) \\
^{Eb}multiplied by $\pi$ (multiply) \\
Multiply the integral by $\pi$! ^{F#7}($\pi\textsuperscript{3}$) \\
^{Hm}$\Pi$ ^{A7}tastes ^{D}real ^{Db7}good ^{Gb7}with ^{B7}whipped ^{Eb}cream! \\
Mama-Mia, Mama-Mia ^{Eb}Mama ^*{Ab}Mi ^{Eb}a ^{Ddim}let ^{Cm7}me ^{B7}go. \\
Pre-^*{Eb}calcu ^{Ab}lus did not ^{D7}help me to ^{Gm}prepare for ^{B7}Calculus, ^{B7}for Calculus, help me! \\
\end{verse}
(Interlude)
Další epická mezihra
\begin{verse}
So you think you can find out the limit of $y$? \\
So you think youll find zero and have it defined \\
Oh baby cant define that point baby \\
Its undefined Goes to positive and negative infinity \\
Oooh. Oooh yeah, oooh yeah. Differentiation \\
Anyone can see Any mere equation \\
It is differentiable for me. \\
(Any way this graph goes) \\
^{B}So you think you can find out the ^{Eb}limit of ^{B}$y$ ^{Db}? \\
^{B}So you think you'll find zero and ^{Eb7}have it de^{Ab}fined \\
^{Fm}Oh ^{B}baby ^{Fm}can't define that point ^{B}baby \\
^{Fm}It's unde^{Bm}fined ^{Fm}Goes to positive and ^{B}negative in^{Eb}finity \\
\end{verse}
\begin{verse}
^{Eb}Oooh. ^{Bdim7}Oooh ^{Cm}yeah, ^{Bdim7}oooh ^{Cm}yeah. \\
^*{Cm}Differentia ^{Gm}tion. ^{Cm}Anyone can ^{Gm}see \\
^{Cm}Any mere equai^{Abm}tion ^{Ab}It is differentiable for ^{Eb}me. \\
^{Bb}(Any ^{F}way this ^{Ab}graph ^{Gm7}goes ^{F}) \\
\end{verse}
\end{song}