Calculus Rhapsody
Phil Kirk & Mike Gospel
Is this x defined? Is f continuous? How do you find out? You can use the limit process. Approach from both sides, The left and the right and meet.
Im a just a limit, defined analytically Functions continuous, Theres no holes, No sharp points, Or asymptotes.
Any way this graph goes It is differentiable for me for me. All year, in Calculus Weve learned so many things About which we are going to sing We can find derivatives And integrals And the area enclosed between two curves.
Y prime oooh Is the derivative of y Y equals x to the n, dy/dx Equals n times x
To the n1. Other applications Of derivatives apply If y is divided or multiplied You use the quotient And product rules And dont you forget To do the dance Also oooh (dont forget the chain rule) Before you are done, You gotta remember to multiply by the chain
[Instrumental solo]
I need to find the area under a curve Integrate! Integrate! You can use the integration Raise exponent by one multiply the reciprocal Plus a constant Plus a constant Add a constant Add a constant Add a constant labeled C (Labeled Ceeeeeeee)
Im just a constant Nobody loves me. Hes just a constant Might as well just call it C Never forget to add the constant C Can you find the area between f and g Integrate f and then integrate g (then subtract) To revolve around the yaxis (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! MamaMia, MamaMia MamaMia let me go. Precalculus did not help me to prepare for Calculus, for Calculus, help me!
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)

Bohemian Rhapsody
Queen
Is this the real life? Is this just fantasy? Caught in a landslide No escape from reality Open your eyes Look up to the skies and see
I’m just a poor boy (Poor boy) I need no sympathy Because I’m easy come, easy go Little high, little low
Any way the wind blows Doesn’t really matter to me, to me
Mama just killed a man Put a gun against his head Pulled my trigger, now he’s dead Mama, life has just begun But now I’ve gone and thrown it all away
Mama, ooh Didn’t mean to make you cry If I’m not back again this time tomorrow Carry on, carry on as if nothing really matters
Too late, my time has come Sends shivers down my spine Body’s aching all the time Goodbye, everybody I’ve got to go Gotta leave you all behind and face the truth Mama, oooooooh (Anyway the wind blows) I don’t want to die Sometimes wish I’d never been born at all
[Guitar Solo]
I see a little silhouetto of a man Scaramouch, Scaramouch, will you do the Fandango Thunderbolt and lightning, very, very frightening me (Galileo) Galileo (Galileo) Galileo, Galileo Figaro Magnificooooo I’m just a poor boy nobody loves me He’s just a poor boy from a poor family Spare him his life from this monstrosity
Easy come, easy go, will you let me go? Bismillah! No, we will not let you go Let him go Bismillah! We will not let you go Let him go Bismillah! We will not let you go Let me go (Will not let you go) Let me go (Will not let you go) (Never, never, never, never) Let me go, o, o, o, o No, no, no, no, no, no, no (Oh mama mia, mama mia) Mama Mia, let me go Beelzebub has the devil put aside for me, for me, for me!
So you think you can stone me and spit in my eye So you think you can love me and leave me to die Oh, baby, can’t do this to me, baby Just gotta get out, just gotta get right outta here
[Guitar Solo] (Oooh yeah, Oooh yeah)
Nothing really matters Anyone can see Nothing really matters Nothing really matters to me
Any way the wind blows…
