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Browse Classroom Capsules and Notes

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Displaying 1121 - 1130 of 1211

The Derivatives of Arcsec \(x\), Arctan \(x\), and Tan \(x\)

Using geometry to find the derivatives of inverse trigonometric functions

A Nonstandard Solution to a Standard Problem

An alternative way of finding the equation of the circle.

Some Interesting Consequences of a Hyperbolic Inequality
Using Geometry to find the proof.
Trees and Tennis Rankings
The author uses combinatorics to find the number of rankings of tennis players that are consistent with the tree representing a given tournament.
Counterexamples to a Comparison Test for Alternating Series

Example to clarify concept of alternating series.

A Note on Differentiation

A different way to find the product rule

Classifying Row-Reduced Echelon Matrices

The author characterizes and counts the number of the many row-reduced echelon forms associated with the set of all \(m \times n\) matrices.

Using Riemann Sums in Evaluating a Familiar Limit

A different way to find a usual limit

Three Ways to Maximize the Area of an Inscribed Quadrilateral
Use trigonometry inequality to show a geometric fact.
Irrationality Made Easy

An alternative criterion to determine if a number is irrational

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