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Browse Classroom Capsules and Notes

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Displaying 1191 - 1200 of 1214

The author provides a characterization of \(n\)-dimensional quadratic functions in terms of tangent planes.

A mysterious pattern when \(\tan x\) tends to infinity is found and explained in terms of L'Hospital's rule.
It is shown that Euler-Cauchy equations with certain types of nonhomogeneous terms can be solved by the method of undetermined coefficients.
The author describes the shape of an overhead cable suspended from a horizontal deck with non-uniform lineal mass.
The author finds a more effective way to deal with partial fractions with an irreducible quadratic denominator.

The authors provide a geometric proof for the limit , \(\frac{\sin t}{t}\), simpler than the geometric proof found in most calculus textbooks.

Find the probability of winning a game.
The author presents a visual proof of the well-known formula for the sum of the first n cubes.
It is shown that (b - a)/(ln b - ln a) fits between the arithmetic and geometric mean.