Mark Thornber

“Sing epsilon delta, Stewart and Tall” (Google it!)

Graham Cumming posted a long thread on X today, with his best guesses as to what went wrong and why things turned out as badly as they did. I suspect he is right on all counts!

#FridayFive
1. Long Hot Summer - Tom Robinson Band
2. I Am A Town - Mary Chapin Carpenter
3. Here Comes the Sun - The Beatles
4. If You Can’t Stand The Heat - Bucks Fizz
5. Summer Breeze - The Isley Brothers

OCR follows Rudin etc.
Item 8.01c on the specification states:
‘“Divergence” can refer to sequences that are bounded or unbounded.’

I don’t think this is correct. Here is professor Peter Coles (a Newcastle lad) with the original Latin and the translations.
https://telescoper.blog/2019/11/13/newtons-laws-in-translation/

This list worked for me
https://bhi.co.uk/repairer/

Are cointerior angles really equal?

Out Now: 'A Tribute to Nick Lord' celebrating his work within the Mathematical Gazette and his contributions to the MA. Printed copies from £7, with the eBook free to MA members, or for just £1 to non-members.

Printed: members.m-a.org.uk/Shop/product...
eBook: members.m-a.org.uk/Shop/product...

For polynomials, tangent lines can be found by looking for repeated roots. No need for limits.
We find m so that p(x)-p(a)=m(x-a) has a repeated root.
This gives m=p’(a)
For quadratics it’s good old b^2-4ac=0

It’s definitely a US thing. Just check any of their doorstep-sized textbooks.
I always thought it was easier to remember than concave/convex, but confusion arises later when convex is used to mean “the curve is under the chord”

There are a number of similar triangles. The ratios of corresponding lengths will be equal.

See my previous reply.

Lists are arrays. You can access individual items with indexing. For example L1[2]

I usually buy direct from the Double Two website. Lots of colours available
https://www.doubletwo.co.uk/mauve-long-sleeve-non-iron-cotton-rich-shirt/

The first 3 terms are (z-3)^2+1. Try the substitution u=z-3, followed by completing the square.

You should try the Guardian quick cryptic. Each one uses 4 different clue types and they give examples of each.

https://www.theguardian.com/crosswords/series/quick-cryptic

There’s a typo in 2a) …

#FridayFive
1. On the Dark Side - Eddy and the Cruisers
2. Power In The Darkness - Tom Robinson Band
3. Because the Night - Patti Smith
4. Corcovado (Quiet Nights of Quiet Stars) - Getz, Gilberto
5. Dancing In The Dark - Cannonball Adderley

We have seen issues with this in the past. Some courses at some universities want to make offers on 3 A levels taken at the same time. Medicine has been a problem here.

I do this in Excel
1) create a scatter graph with a single point
2) use series properties to make the point invisible
3) use axis properties to get scales and labels correct
4) use major and minor grid line properties to get the grid lines looking nice
You can export to Word

#FridayFive
1. The Only Living Boy in New York - Simon and Garfunkel
2. My Friend Stan - Slade
3. Whatever Happened To You - Highly Likely
4. There’s a Light Beyond These Woods (Mary Margaret) - Nanci Griffith
5. Woody and Dutch on the Slow Train to Peking - Rickie Lee Jones

The contract had a penalty clause of £12000 per day for every day it ran over the agreed finish date. They finished on time!

When my school was rebuilt we took our FM classes to visit the site manager. He showed us a huge stack of Gantt charts for every part of the project. They tracked the number of workers used by every subcontractor every day and updated the charts every night.

#FridayFive
River - Joni Mitchell
Gaudete - Steeleye Span
Mary’s Boy Child - Harry Belafonte
I Believe In Father Christmas- Greg Lake
Merry Christmas Darling- The Carpenters

I integrate by parts

https://www.youtube.com/watch?v=-reFBJ4R9iA

#FridayFive
1. Winter Song - Lindisfarne
2. The Snow It Melts The Soonest - Anne Briggs
3. Mother Russia - Renaissance
4. Snowbound - Genesis
5. Under Ice - Kate Bush

Box plot - Wikipedia

The box and whiskers plot was first introduced in 1970, after all the hypothesis testing stuff.
en.wikipedia.org/wiki/Box_plot

Not needed on lines 1 or 2 because it is contained in/implied by the integral on the right.
Needed on line 3 because the LHS is indefinite, but the RHS as written is definite.

Simple numerical approximation:
1.4^2=1.96 so sqrt(2)>1.4
pi/4>3/4=0.75
sum>2.15>2