﻿﻿ calculus – futurebird

## Almost Convergence.

The title of my last post "Almost Cauchy Sequence" made me wonder if "Almost Cauchy" was already defined in some formal sense. I could not find much on "Almost ...

## Almost Cauchy Sequence, unfinished business.

I just remembered a question from beginning analysis that my professor mentioned in class: "Find a sequence that is not Cauchy, yet any consecutive terms will b...

## Extending L' Hopital. (For my students. )

How can one deal with ? It appears to be the indeterminate form . The graph shows that it has a nice limit: (Notice, how this function produces imaginary vales ...

## Looks can be deceiving!

Look at the graph in the previous post. I was right! They don't intersect at a common point, rather the limit of the consecutive intersections is . This is just...

## Points that call out to you.

, , ... You get the idea. Naturally I want to know what those intersections are! I need to go for a run before it gets dark, but It seems that if we fix x=1 the...

## Quickie.

A curve A is orthogonal to B is the tangent lines at their intersections are perpendicular. Thinking of the follium of Descartes again, give the equation for a ...

## Rational points on the folium.

My students are studying implicit differentiation, we look at the folium of Descartes: They found the equation of the tangent at For their homework I want to ha...