\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 Weve ^{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}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}$C$ \\ \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! \\ \end{verse} (Interlude) \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) \\ \end{verse} \end{song}