# Browse Classroom Capsules and Notes

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Displaying 21 - 30 of 225

How do sequences of the form $(1+x/n)^{n+\alpha}$ with $x >0$ approach their limits?

The authors exhibit two differentiable functions for which the integration by parts formula does not apply.

The author shows how to solve a class of analytic functions using an approach demonstrating a surprising connection between multivariable calculus and linear algebra.

The derivative of arctangent is derived directly from the definition of derivative by using some clever inequalities.

Without using double integrals, a new method is presented to evaluate the two Fresnel integrals about sine and cosine that has a wider applications than previous methods.

A proof without words approach to the geometric-arithmetic mean inequality

A weighted arithmetic/geometric mean inequality is proved.

The authors discuss the evaluation of certain improper integrals by first transforming them.

The article attempts to explain why exponential functions were chosen to define hyperbolic functions.

For what positive number $x$ is the $x$-th root of $x$ the greatest?