Distances on Earth 3: Planar Approximation

We’ve looked at two formulas for the distance between points given their latitude and longitude; here we’ll examine one more formula, which is valid only for small distances. This is a “flat-earth approximation” to distance.

Average Rate of Change of a Function

(A new question of the week) Average rate of change is a topic taught in pre-calculus and calculus courses, primarily as preparation for the derivative, though it has more immediate applications. A recent question asked about when the concept is valid, which I found interesting.

Help with Factoring: Trinomials

(A new question of the week) I recently had a pleasant discussion of factoring, with the kind of student for whom I returned to teaching: one who has been away from math for a while, and with greater maturity has the determination to succeed. We’ll see several examples of the “ac-grouping” method of factoring a …

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Implicit Differentiation: Explanation, Examples, and a Surprise

In response to a recent request for information about implicit differentiation (hi, Brian!), let’s take a look at that topic. It happens to be distantly related to Friday’s topic, which was about implicitly defined curves. We’ll start with a thorough explanation, and then look at several specific examples, capping it off with a weird one.