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 n-1.
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 C-ee-ee-ee-ee)

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
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!

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
Magnifico-o-o-o-o
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…