# Browse Classroom Capsules and Notes

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Displaying 81 - 90 of 225

Using derivatives, the author shows the relationship in space between the volume and the surface area and in the plane between area and the perimeter.

The author uses differentiation to find the point of tangency for exponential functions for all bases and shows they lie on a horizontal line.

Computing a certain limit for areas of a sector. Note that the first displayed limit is as $\theta \rightarrow 0$, not as $\theta \rightarrow \infty$ .

The article shows how to maximize the arclength of the trajectory of a cannonball.

The author shows how to use a CAS to discover improved numerical integration methods for low-degree polynomials.

The author shows that The Intermediate Value Theorem, The Maximum Value Theorem, and The Mean Value Theorem all fail for functions continuous on the rationals.

The author gives an elementary proof of the chain rule that avoids a subtle flaw.

Find the averages of the distances with respect to different variables.

The author describes a simple way to find the derivative of $\sin \theta$.

The authors use the Monotonicity Theorem to prove that there is a unique monthly payment that exactly matches the amortization parameters.