Calculus Rhapsody

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
I'm just a limit
Defined analytically
Function’s continuous
There’s no holes
No sharp points
Or asymptotes
Anyway this graph goes
It is differentiable for me
For me

All year, in calculus
We’ve learned so many things
About which we’re going to sing
We can find derivatives
And integrals
And the area enclosed between two curves
Y’, ooh
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 don’t you forget to do the dance
Also, ooh
(Don’t forget the chain rule)
Before you are done
You gotta remember
To multiply by the chain

I need to find the area under a curve
Integrate! Integrate!
You can use the integration
Raise the exponent by one
Multiply the reciprocal
Add a constant. Add a constant
Add a constant. Add a constant
Add a constant labeled c
Labeled c

I'm just a constant, nobody loves me
He’s 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 y-axis
Integrate outer radius
Minus inner radius squared
(Multplied) 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!
Precalculus did not help me prepare for
Calculus, for calculus, help me!

So you think you can find out the limit of y?
So you think you’ll find zero and have it defined?
Oh baby, can’t define that point baby
It’s undefined
Goes to positive and negative infinity

(Ooh yeah, ooh yeah)
Differentiation, anyone can see
Any mere equation
It is differentiable for me
Any way this graph goes