(A new question of the week) We usually see limits applied to functions in a calculus class. An interesting question from late October deals with a limit in a geometrical construction based on a function. We’ll be seeing how to discover a proof, then several alternative proofs, and finally what the answer means.
Last week, we looked at two solutions to the problem of finding the probability that you can make a triangle using three pieces of a stick, if we cut it at two independently chosen, random locations. This time, we look another solution to that problem, and a similar solution to the version in which we …
This week we look at questions about how likely it is that you can make a triangle out of three random pieces of a stick. As always in probability, the first issue comes in deciding how the process is to be done (that is, what does it mean to break a stick randomly?); we’ll also …
(A new question of the week) A good way to check (and hopefully build) a student’s depth of understanding is to assign non-routine problems, in which familiar ideas are twisted around so you have to come at them from a different direction. Here we’ll look at a question about a graph that can be solved …
In our series on averages, last week we introduced the idea of the weighted average (or weighted mean), where each item has a weight attached. The classic examples all involve grade averages in various ways. This time, we’ll look at how weighted averages arise when you need to average several averages together, something we touched …
(A new question of the week) Let’s look at a quick question from mid-September, that had a number of different answers. In some ways, this is an easy question; but we’ll take it a little further, so keep reading to the end.
To close out this series on the definition of the derivative, I want to look at a few questions about alternative versions of the definition, primarily the “symmetric difference quotient”. We’ll see that this leads to a slightly different result, not always equivalent to the original, and we’ll observe some associated ways that calculators can …
(A new question of the week) We have had a lot of interesting questions recently. This one involved inverse trigonometric equations that led to cubic and quartic equations. We’ll observe here one of the benefits of embedding the original discussion in a blog format where I can add information that will help you, the reader, …
Challenging Inverse Trig and Polynomial Equations Read More »
(An archive question of the week) We’ve looked at the scalar (dot) product and the vector (cross) product; but there is one answer in the Ask Dr. Math archives that was too long to fit in either post. Here we’ll see again where the two familiar products come from, while looking deeper into the math …
Having just looked at how to solve oblique triangles, let’s look at a couple “word problems” (applications) involving such triangles. We’ll be using the Law of Sines, and also exploring alternative methods of solution.