# Browsing category ask uncle colin

Dear Uncle Colin, I need to find four consecutive numbers such that the first is a multiple of 5, the second a multiple of 7, the third a multiple of 9 and the fourth a multiple of 11. Can you find such a number? - Summing Up Needs Zero Intelligence

## Ask Uncle Colin: An Arcsine Inversion

Dear Uncle Colin, I’m trying to invert $y = \arcsin\br{x^2 + 4x - 5}$, but I get stuck at $x^2 + 4x = \sin(y) + 5$. Any pointers? - All Routine Calculations Should Invert Naturally Hi, ARCSIN, and thanks for your message! Just before I dive into this, I have

## Ask Uncle Colin: A Horrible-looking Limit

Dear Uncle Colin, I need to work out $\lim_{x\to\infty} \left\{ \left[ \frac{ 2^{1/x} + 8^{1/x} }{2} \right]^x \right\}$. The textbook says it’s four, but my engineering friends all get different answers. How would you work it out? - Giving Engineers Real Maths Analysis Is Naive Hi, GERMAIN, and thanks for

## Emergency Ask Uncle Colin: What happens now?

Dear Uncle Colin, I’m meant to be sitting my A-levels this summer and there’s an awful disease going around. I don’t know if school will be open next week or even if the exams will go ahead. I don’t know what that means for university. I’m scared. What do I

## Ask Uncle Colin: Long Division in Base 5

Dear Uncle Colin, I’ve been asked to show how to do $23241 \div 31$ in base 5 by long division - I can barely do it in base 10! Help! - Lots Of Number Games Hi, LONG, and thanks for your message! There are several steps to working a long

## Ask Uncle Colin: A Pointy Thing

Dear Uncle Colin, What do you call the ‘point’ of the absolute value graph - for instance, $(0,0)$ on the graph of $y=|x|$? It can’t be a minimum because the gradient is undefined! Proof Or It’s Not True Hi, POINT, and thanks for your message! I hate to go ‘well,