Rating is available when the video has been rented.
This feature is not available right now. Please try again later.
Published on May 22, 2009
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
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.