(A new question of the week) I intended to fit three problems into last week’s post, but the third was too interesting to shorten, so I’m posting it separately. The problem itself is not hard, but in looking for a more direct solution, we extend it, discovering (through geometry software) more general facts, which lead …
(A new question of the week) Several interesting geometry problems about triangles and circles came in recently. We’ll look at two today, and a third next week.
(A new question of the week) We often solve basic trigonometric equations; but a recent set of questions dealt with challenging trigonometric inequalities, which bring with them a new set of issues. We’ll look at several of those here, which combine trig with polynomials, rational functions, and more. Each will illustrate something new to watch …
(A new question of the week) Riemann sums are used in defining the definite integral. But they can also be used in reverse: Sometimes you can be given the limit of a summation and asked to read it as a Riemann sum, and then turn it into an integral. Usually this is fairly straightforward; but …
(A new question of the week) Extraneous roots can not only confuse the final solution to a problem; they can also make it harder to solve in the first place if you don’t deal with them early. Here is a relatively complicated rational equation, two questions about its solutions, and several ways to make it …
A Rational Equation, With and Without Extraneous Roots Read More »
A recent question (whose asker refused to cooperate by showing work, so that we were unable to help) reminded me that we haven’t yet shown a similar kind of problem that can be quite interesting: problems where we are given the value of one or several expressions in several variables, and are asked for the …
Here is a short discussion of a common type of problem in trigonometry classes: finding a trig function of the sum or difference of two angles, given minimal information about them.
(A new question of the week) Here is an interesting collection of problems involving logarithms with different bases, which require some unique thinking. And after we’d worked out a good strategy, another problem arose at a whole new level.
A question just after we recently discussed quartic equations, has special features that lead to a unique solution method. We’ll be showing how to use synthetic division, and seeing some interesting graphs.
(A new question of the week) Last week I discussed several Ask Dr. Math questions about factoring quartic polynomials, which had been on my list of potential topics. That list also included a question on that topic from three years ago, that didn’t make it into the blog at the time. That will lead us …