# Browse Classroom Capsules and Notes

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Displaying 41 - 50 of 1135

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

Using a generalized Fibonacci sequence to determine the expected number of tosses of a fair coin to first obtain $$n$$ consecutive heads

Examples of an elementary transcendental function having three different kinds of asymptotes $$x-a-0, y-b=0, y=mx+c$$ and defined by one single equation in its domain of definition

A simple, natural way to geometrically read off the complex roots of a real quadratic equation

Using the Arithmetic-Geometric Means Inequality and the Mean Value Theorem to show that the maximum value of $$x^{1/x}$$ occurs at $$x = e$$