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Browse Classroom Capsules and Notes

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Displaying 31 - 40 of 47

If a function of one variable has a unique critical point, then it is not only a local max/min, but global. Does the same hold for functions of two variables? The authors provide a...

Using polar curves, the author defines "vertex solids", which include usual cones and paraboloids, and computes their volumes.

Some popular optimal value and constraint problems, like fence-area problem and box-volume problem, are generalized to \(n\)-dimensions.

The author derives formulas for the coefficients of the characteristic polynomial of a square matrix in terms of the partial derivatives of its determinant, which is viewed as a function of...

Three propositions, involving integration and partial differentiation, one of them Fubini`s Theorem, are shown to be equivalent.

The authors "describe two different methods for locating the centroid of a finite number of given points ... without using coordinates or numerical calculations". Some examples are...

Ptolemy's Theorem states that the product of the diagonals of a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle) is equal to the sum of the products of the opposite sides...
The author uses the concept of maximum and minimum values to find Fermat points for a triangle. (The Fermat point of a triangle is the point such that the distances from the vertices have a...

An alternative way to evaluate the famous improper integral of Gauss, \(\int_{0}^{\infty} e^{-x^2} dx\)

The author classifies the quadratic forms defined by simple 2 by 2 matrices and illustrates them with corresponding quadratic surfaces.

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