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Browse Classroom Capsules and Notes

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Displaying 191 - 200 of 1211

A Note on Integration by Parts

Skirt integration by parts using a method of undetermined coefficients.

Relating Differentiability and Uniform Continuity
F is differentiable at a if and only if the difference quotient is uniformly continuous.
Both a Borrower and a Lender Be

Payments on loans also generate continuous interest type problems.

Arithmetic Progressions and the Consumer
A bothersome discrepency regarding arithmetic progressions is cleared up.
More Applications of the Mean Value Theorem

Inequalities by applying the mean value theorem to \(\ln x\)

Cantor's Disappearing Table

A cantor-like procedure makes a table vanish by removing less than half of it.

Bernoulli's Inequality and the Number \(e\)

Convergence of sequences approaching \(e\), with no mention of \(\ln x\)

Area of a Parabolic Region

A general formula for that area of a parabola in terms of its parameters

Digital Roots of Mersenne Primes and Even Perfect Numbers

This note links two previous papers on Mersenne primes and digital roots.

An Algebraic Approach to Partial Fractions
Finding the partial fraction expression

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