Browse Classroom Capsules and Notes

You can filter the list below by selecting a subject category from the drop-down list below, for example by selecting 'One-Variable Calculus'. Then click the 'APPLY' button directly, or select a subcategory to further refine your results.

Displaying 1081 - 1090 of 1211

Filter by subject

Divergence of the Harmonic Series by Rearrangement

A quick proof of the divergence of the harmonic series

Exploiting a Factorization of \(x^n - y^n\)

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

The Pen and the Barn

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.

On Dividing Coconuts: A Linear Diophantine Problem

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

Halley's Gunnery Rule

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

Introduction to Limits, or Why Can't We Just Trust the Table?

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

Some Sums of Some Significance

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

A Rose is a Rose is a Rose...

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

Area and Perimeter, Volume and Surface Area

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.

Cylinder and Cone Cutting

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