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Browse Classroom Capsules and Notes

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Displaying 1 - 10 of 225

In this note the authors present an elementary proof that the inequalities \( (1+1/n)^n < e \leq (1+1/(m-1))^m \) hold for \(n>0\) and \(m>1\), using only the arithmetic-geometric mean...

This capsule discusses the mathematics of a real-life experience with dogs playing fetch into the water. The leap-off point chosen by the dog turned out to ones that will either minimize the...

This capsule introduces a straightfoward way of calculating partial fraction decomposition for functions of specific forms by long division. The obtained partial fractions can be easily...

This article generalizes a problem of dogs fetching a ball in the water and presents it as a problem of calculus of variation.

A technique is introduced for the purpose of finding the relative maximum values of the probability density function. The crux is to find the critical numbers of the exponential of the...

An example in business calculus is used to show a short-cut to compute the discrepancy between the difference of values and the differential for certain class of functions.

Certain p-series are the focus of this capsule. This project comes with scenarios to help students "visualize" the convergence or divergence of the p-series.

This capsule  started with two coffee cups that are complenetary, i.e., their profiles fit together. The author then explores the condition in which the two cups, obtained as solids of...

This capsule discusses a way to show each non-zero element of certain rings have a multiplicative inverse. The approach is to set up a system of linear equations and the solution is the...

A visualization of the triple angle formulas for sines and cosines is presented.

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