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WCEastFZX favorited a video
(1 month ago)
Calculus Rhapsody
By Phil Kirk & Mike Gospel
Is this x defined?
Is f continuous?
How do you find out?
You can use the limit process.
Approach from bo...
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Calculus Rhapsody
By 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)
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WCEastFZX favorited a video
(2 months ago)
An awesome rap video about integration (as used in physics and calculus).
Go, go, go, go, go, go, go Burnsie
It's your birthday
We gonna party like it...
more
An awesome rap video about integration (as used in physics and calculus).
Go, go, go, go, go, go, go Burnsie
It's your birthday
We gonna party like it's your birthday
We gon' draw free bodies like it's your birthday
And we gon' take the area cuz it's your birthday
CHORUS:
You'll find us in da club, rockin' math club
You've seen dy/dx but that's not enough
We're into f of x if it's gettin' bumped up
So integrate with us if you're into areas, yeah
We're in da club, rockin' math club
You've seen dy/dx but let's back it on up
We're into f of x if it's gettin bumped up
So integrate with us if you're into areas, yeah
So here's your line, with a steady slope
Integrate it, it's a triangle - Man, that's dope
Integrate acceleration, there's your speed
Integrate again if it's distance you need
Do it once more? -- How about not
Fine, we'll save it for calc --Yeah, man, that's what I thought
Can we integrate cos? -- Yeah, that's sin, G
Aren't you forgetting something? -- Oh yeah -- PLUS C!
Integration's derivation backwards, y'all
Area under a curve and that's all
Find it from a limit to a limit, that's it
If you can't do that then you can't do -- ANYTHING!
Area underneath the grading curve
Equals the people who can't do this and they're where they deserve
But don't give up now, cuz how can you expect
To wow the people grading your AP test
CHORUS
DANCE TIME!
Girl, how much junk do you lunk in dem jeans?
Let's find out, and by that I mean
If your jeans are expressed by a function of x
That is 4x^3 + 3x^2 + x
Then the volume amassed by your gigantic -- HEY!
Has a maximum value of -- DAMN!
And by that he means x^4 + x^3 + (1/2)x^2 -- PLUS C!
CHORUS
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