# Browse Classroom Capsules and Notes

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Displaying 121 - 130 of 1212

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 $x = e$

Using induction to investigate the symmetric difference of $n$ sets