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.

How Do You Simplify a Fraction?

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 …

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L’Hôpital’s Rule: What and Why

The next few posts will look at a powerful technique for finding limits in calculus, called L’Hôpital’s Rule. Here, we’ll introduce what it is, and why it works. In the next post we’ll examine some harder cases. Indeterminate forms The method we will be discussing is used to find limits that have an indeterminate form. …

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