Last week we looked at Ask Dr. Math questions about homogeneous linear recurrences; this time we’ll see some on simple (first-order) non-homogeneous recurrences, which will bring us back to the topic two weeks ago, when we looked at the examples of this type that a student had the most trouble with. This will be an …
Last week we looked at a recent question about recurrence relations, and I realized it needs a companion article to introduce these ideas. So here we will look at some answers from Ask Dr. Math about the simpler case, including general methods, why they work, and applications.
(A new question of the week) A recent question asked us to find errors in solving recurrence relations by the method of undetermined coefficients. We’ll see several things that can go wrong, and correct some misunderstandings.
(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 …
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.
Last time we looked at solving triangles in the ASA, AAS, SSS, and SAS cases. We have one more case, which tends to be a little more complicated: the “ambiguous case”, SSA. SSA: Two sides and the angle opposite one of them We’ll start with this question from 1998: Triangles and Law of Sines I …
Having just looked at the Law of Sines and the Law of Cosines, let’s consider how they can be applied to solving an oblique triangle – that is, finding missing parts of a triangle that is not a right triangle. The Ask Dr. Math site’s Trigonometry FAQ includes a concise summary of a procedure for …
Last time we examined the basic concept of equivalent fractions – the fact that different fractions can represent the same value. We saw that there will be one way to write a fraction that is “in lowest terms” – no other fraction with the same value will involve smaller numbers, and all the others can …
(A new question of the week) This week and next I will look at a recent discussion on trigonometry that dug deep into two different issues: solving equations, and proving identities. These are good summaries of how to approach these common kinds of problems. This week: solving basic trig equations. Questions about trig functions Here …
Last time we looked at the basics of L’Hôpital’s Rule, which applies to limits of the form or , and ways to understand or prove it. Here, we’ll consider a variety of questions we’ve received about less direct application of the rule. We’ll see ways to apply it to other indeterminate forms (, , ), and what …