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 ...
Tag: calculus
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...