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.

Normal Approximation … or Not?

(A new question of the week) A recent question (from May) about approximating the binomial distribution with the normal distribution led to some (accidental and otherwise) insights about the method. I have to solve this problem: A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan …

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Domain, Range, and Quadratic Inequalities

(A new question of the week) We had a long discussion last August about domain and range of functions involving either quadratic functions or restricted domains (or both). Two Math Doctors got involved, offering different ways to approach the same problem. I’ve edited the discussion to avoid some intermingling of topics. A quadratic inequality Here …

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