# Browse Classroom Capsules and Notes

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Displaying 111 - 120 of 1209

The paper presents a guided collection of problems investigating when groups are isomorphic to proper subgroups.

The author explores integration of radially symmetric functions of several variables.

This is a discusion of the importance of the existence of limits in L'Hôpital's Rule.

An analytic proof of the fact that for any triangle $$ABC$$, $$G=\frac{1}{3}(A+B+C)$$ is the centroid of the triangle.

A simple characterization of the condition that, for an integer-sided triangle, one angle is twice another.

An alternative to partial fractions for certain integral calculations

Using substitutions to derive equations for the ellipse and hyperbola

A polar coordinate proof of the fact that the focal radii of an elipse (hyperbola) make equal angles with the tangent.

An extension of the fact that $$1/n!$$ is the content (volume) of a particular $$n$$-dimensional simplex

Simple proofs of the formulas for the derivatives of $$\sin x$$ and $$\cos x$$ when $$x$$ is acute