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Browse Classroom Capsules and Notes

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Displaying 121 - 130 of 225

Polar equations for the paths obtained when pursuing persons are positioned originally at the vertices of a regular \(n\)-gon
A simple example of circular area that exhibits the Fundamental Theorem of Calculus

Exercise in parametric equations by group contest of plotting four-letter words

A standard picture proof of the double angle formula for sine and cosine

An example of numerical estimates of tangent line to an implicitly defined function that illustrates the meaning of differentials

A comparison of areas is used to derive the integral formula of the arctangent

A quick proof of the arithmetic-geometric mean inequality using properties of the function \(x^{1/x}\)

Using the power rule for derivatives to prove the Binomial Theorem (instead of the reverse).

An easier and more intuitive proof of the Mean Value Theorem from Rolle's Theorem.
A bug is on the inside of a container that has the shape of a paraboloid \(y=x^2\) revolved about the \(y\)-axis. If a liquid is poured into the container at a constant rate, how fast does the...

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