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' ... 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 don't you forget to do the dance ... Also ... oooh (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. (Oooh yeah, Oooh yeah) Differentiation, anyone can see Any mere equation It is differentiable for me. Any way this graph goes.