Month: April 2026

What Are Hyperbolic Functions?

Hyperbolic functions are functions that form a sort of parallel universe to the trigonometric functions. They are typically introduced as an aside while teaching calculus – because they happen to be useful there, and also because they can’t really be understood without calculus. As a result, we can easily misunderstand them, forget about them, and …

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Solving Polynomial and Rational Inequalities

A recent question asked about quadratic inequalities; we’ve touched on that in Domain, Range, and Quadratic Inequalities, but here we’ll introduce three basic approaches. We’ll follow that with old questions about polynomial inequalities (mostly quadratic) and rational inequalities (fractions), expanding on the basic methods.