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Browse Classroom Capsules and Notes

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Displaying 121 - 130 of 1213

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 \(x = e\)

Using induction to investigate the symmetric difference of \(n\) sets

An elementary proof of Heron's Formula