Posted in ask uncle colin.

Dear Uncle Colin, I'm told that the graphs of the functions $f(x) = x^3 + (a+b)x^2 + 3x – 4$ and $g(x) = (x-3)^3 + 1$ touch, and I have to determine $a$ in terms of $b$. Where would I even start? – Touching A New Graph Except Numerically Troubling

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Posted in integration.

Some while ago, I showed a slightly dicey proof of the Basel Problem identity, $\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac {\pi^2}{6}$, and invited readers to share other proofs with me. My old friend Jean Reinaud stepped up to the mark with an exercise from his undergraduate textbook: The French isn't that difficult,

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Posted in ask uncle colin.

Dear Uncle Colin I've been asked to find $\sum_3^\infty \frac{1}{n^2-4}$. Obviously, I can split that into partial fractions, but then I get two series that diverge! What do I do? – Which Absolute Losers Like Infinite Series? Hi, WALLIS, and thanks for your message! Hey! I'm an absolute loser who

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Posted in podcasts.

In this month's episode of Wrong, But Useful, Colin and Dave are joined by @niveknosdunk, who is Professor Kevin Knudson in real life. Kevin, along with previous Special Guest Co-Host @evelynjlamb, has recently launched a podcast, My Favorite Theorem The number of the podcast is 12; Kevin introduces us to

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Posted in probability.

This post is inspired by a Futility Closet article. Do visit them and subscribe to their excellent podcast! Suppose you're dealt a bridge hand1, and someone asks whether you have any aces; you check, and yes! you find an ace. What's the probability you have more than one ace? This

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Posted in ask uncle colin.

Dear Uncle Colin I have been asked to describe how $y = \frac{3x^2-1}{3x+2}$ behaves as $x$ goes to infinity. My first answers, "$y$ goes to infinity" and "$y$ approaches $x$", were both wrong. Any ideas? – Both Options Reasonable, Erroneous Limits Hi, BOREL, and thanks for your message! My first

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Posted in algebra.

One of the more surprising results a mathematician comes across in a university course is that the infinite sum $S = 1 + \frac{1}{4} + \frac{1}{9} + … + \frac{1}{n^2} + …$ comes out as $\frac{\pi^2}{6}$. If $\pi^2$s are going to crop up in sums like that, they should be

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Posted in ask uncle colin.

Dear Uncle Colin, What is $\frac{1}{\infty}$? – Calculating A Number, Though Outside Reals Hi, CANTOR, and thanks for your message! The short answer: it's undefined. The longer answer: Infinity is not a number. It's not something you're allowed to divide by. The calculation doesn't make sense, and writing it down

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Posted in ninja maths.

"So," said the Mathematical Ninja, "we meet again." "In fairness," said the student, "this is our regularly-scheduled appointment." The Mathematical Ninja was unable to deny this. Instead, it was time for a demand: "Tell me the square root of 22." "Gosh," said the student. "Between four-and-a-half and five, definitely. 4.7

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