\begin{song}[remember-chords=false]{title={Calculus Rhapsody}, music={Queen}, lyrics={Phil Kirk \& Mike Gospel}} \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. \\ ^{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. \\ ^{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. 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}$y$ \\ $y$ ^{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 \\ 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} \\ \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. \\ \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 $C$. \\ (Labeled $C$-ee-ee-ee-ee) \\ \end{verse} \begin{verse} ^{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} ^{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} Další epická mezihra \begin{verse} ^{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}