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Browse Classroom Capsules and Notes

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Displaying 1081 - 1090 of 1211

A quick proof of the divergence of the harmonic series

A new proof of the binomial identity is given and the method is applied to prove other identities.

In the classical problem of fixed perimeter and maximum area of the calculus, it is shown that the length of the fence affects the shape of the optimal pen.

Two solutions for the classical coconut dividing problem of the five sailors on an island are given.

The author solves the classical problem of firing a projectile through a target situated on an inclined plane.

The author shows with an example that you cannot predict the correct limit by selecting a few values nearby.

The authors discuss certain sums and series that arise in combinatorics and their connections to Sterling numbers.

Plots families of curves in the shape of a roses using parametric and polar plots

Using derivatives, the author shows the relationship in space between the volume and the surface area and in the plane between area and the perimeter.

The author finds the equations for the conic sections by rotating the cone and keeping the plane fixed.