Calculus

Logistic Growth

Last time we looked at the meaning of exponential growth, a term commonly used in describing the initial spread of a virus such as the current SARS2 (which causes COVID-19). But exponential growth can’t continue forever, as it would soon exceed the total population. A slightly more complicated model for growth that takes into account …

Logistic Growth Read More »

Exponential Growth

The term “exponential” has gone viral, so to speak. Do we all know what it means? In the next few posts I’ll look at answers we’ve given to questions about exponential growth and related concepts, some of them about the spread of diseases or rumors. (Disclaimer: I will be writing about the basic math, not …

Exponential Growth Read More »

Derivative as Instantaneous Rate of Change

(An archive question of the week) Last week we looked at a recent question that touched on the idea of the derivative as a rate of change. Let’s look at a long discussion from a few years ago digging into what that means within calculus.

Integrals and Signed Areas

(A new question of the week) This week’s question, asked in January on the new site, will take us through some tricky areas of calculus, and also give a glimpse both of the value of quoting the entire problem you are working on when you ask for help, and of the interesting side discussions we …

Integrals and Signed Areas Read More »

More on 0.999…

(An archive question of the week) In collecting questions and answers about 0.999… for the last post, there were two that were too long to include, but that dig more deeply into issues that some of the standard answers tend to gloss over. So here, I want to look at those two answers, both of …

More on 0.999… Read More »