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WCEastFZX favorited a video
(3 months 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
(4 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...
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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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