To start a series of posts on differentiation (one of the basic concepts studied in calculus), I’d like to look at a number of answers we’ve given to the basic question, What is a derivative? This includes questions about the meaning of the concept and its definition, as well as examples. Something all these questions …
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 …
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 …
(An archive question of the week) While gathering answers to questions about volume and surface area formulas, I ran across this question that applies to all of them: Given all the approximations and assumptions we make in the derivations we show (without calculus), how can we claim that the resulting formula is exact? Or can …
(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.
(A new question of the week) Economics can be a deeply mathematical subject; but as a separate field, it has its own terminology and notation which can sometimes be confusing. Is marginal revenue (or cost, etc.) the same as the derivative of the revenue function, or is it something different? That will be the issue …
(A new question of the week) Sometimes when we are learning a new subject, in this case calculus, a superficially simple question can be confusing. And that can be a good thing! Let’s look at a question about a derivative that, while not using very advanced concepts, gives a challenge to the learner that forces …
(An archive question of the week) I’m going to do something unusual, and post a discussion that was never archived. I ran across it while searching for the original of an archived discussion to check something, and this one stood out as worth posting around the start of the school year. It’s a question from …
(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 …
(A new question of the week) A recent question from a student working beyond what he has learned led to an interesting discussion of alternative methods for solving a minimization problem, both with and without calculus.