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.
Mistakes
Solving an Oblique Triangle, Part 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 …
Why Can’t You Skip the Law of Sines?
(An archive question of the week) I’m in the middle of discussing the Law of Sines and the Law of Cosines, and in searching for questions about them, I ran across one that stands by itself. A student asks his teacher why his method without trig doesn’t work, and gets three answers from us. They …
Intercepts of a Sideways Quadratic
(A new question of the week) Sometimes a topic you think you know looks entirely different in an unfamiliar context. Here, a returning student faces a quadratic equation where x and y are reversed, making the quadratic formula seem foreign! But this is when real learning happens, when you are forced to think through the …
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.
Order of Operations: Common Misunderstandings
Last time I started a series looking at the Order of Operations from various perspectives. This time I want to consider several kinds of misunderstandings we often see.
Frequently Questioned Answers: The Other Child
This is the second in a series on Frequently Questioned Answers – that is, answers we have given that are often challenged by readers, either just out of confusion, or in the form of attacks on our intelligence or honesty. Here, we look at the problem of finding the probability that, given knowledge about one …
Frequently Questioned Answers: Monty Hall
The Ask Dr. Math site includes a Frequently Asked Questions page with extended discussions of common topics like Fractions, Order of Operations, and Prime Numbers. Some topics get a lot of push-back from readers who disagree, some from curiosity, others with virulence. The next few posts will examine our answers to some of these challenges, …
L’Hôpital’s Rule: One More Example
(A new question of the week) Having just looked at L’Hôpital’s Rule, we can conclude with a look at a recent question about it, to illustrate the reality of struggling to apply it (and the process we go through to help a student find an error).
Combining Function Transformations: Order Matters
Last time we looked at questions about how to shift, stretch, or flip a graph by changing the equation of a function. All our examples involved only a single transformation. Now we can look at cases where two or more transformations are combined. As we do this, we will develop a deeper understanding of how …
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