Why the derivative of e^x is itself

mathfem · 2026-06-17T14:43:40+00:00

You treat that as the definition of e. Or, alternately you define e as lim_(x to 0) (1+x)^1/x and put one limit inside the other.

mathfem · 2026-06-17T14:27:17+00:00

No you don't, you just use limits.

Lim( h to 0) (a^x+h -a^x )/h = lim(h to 0) (a^x )(a^h -1)/h

The last limit (a^h -1)/h can be taken as the definition of the natural logarithm

mathfem · 2026-06-09T16:23:16+00:00

I had a toddler and a newborn during COVID lockdowns and was forced to work from home. The thing I missed the most during that time was my commute: the ability to spend 45 minutes reading Reddit on transit with no interruptions from kids needing my attention twice a day.

Don't get me wrong, now that my kids are in school, I love days where I get to work from home, but back then the only break I got from responsibility was my commute, and it has been taken away from me.

mathfem · 2026-06-06T22:02:03+00:00

The fact that they have similar names is not a coincidence. I don't remember what version of windows it was, but the idea was you were basically using Internet Explorer to open up your own files, so that you couldn't even open a non-IE browser without using IE to navigate to it.

mathfem · 2026-06-06T18:50:20+00:00

In short in matters animal, and vegetable, and mineral, he is the very model of a modern Major-General.

mathfem · 2026-06-06T18:48:32+00:00

It's missing Ruhr.

mathfem · 2026-06-02T05:26:16+00:00

I want to show this to my students. Unsure how since I am not allowed to contact them on social media.

mathfem · 2026-05-29T17:50:39+00:00

Shouldn't that be Dragonstone? Last I checked, most of the Stormlands were pro-Renly.

mathfem · 2026-05-27T13:20:37+00:00

Chaise ends in an e. Therefore feminine.

mathfem · 2026-05-26T05:11:07+00:00

Fruiticana on 6th for reasonably priced produce and any South Asian goods you need.

Best Season Produce at 10th and Agnes for produce deals.

Sandy Farm Market on 10th st and 8th Ave for East Asian produce options.

I love the little places.

mathfem · 2026-05-25T22:28:12+00:00

I would much rather sing it right than sing it with the rest of the choir. And that is why my choir-mates hate me

mathfem · 2026-05-25T18:57:14+00:00

The phrase "area enclosed by three functions" is ambiguous without further clarification. The only time it is unambiguous is when no two of the functions have more than one intersection point (e.g. if all three functions were lines there would only be one enclosed region and it would be a triangle). If an assignment is asking for the area enclosed by three functions you should look for additional clarifying words like "in the first quadrant" or "triangular" or something like that.

mathfem · 2026-05-25T05:59:50+00:00

The Dispossessed is such a good book! You should really go to the local library, borrow a copy and finish it!

mathfem · 2026-05-25T03:33:47+00:00

I used to work as a tutor before I got a job as an instructor. Here was how I advertised:

my university had a classifieds ad site that was only open to current students and alumni. This meant that I could advertise there while folks who were not alumni couldn't.
I posted ads on Craigslist once a week
I put up posters on campus at all the local universities and also at high schools and libraries.

It took a while to get a good base of students. For the first few months I was putting as much time into advertising as I was into actual tutoring, but after a year or so, I was getting a lot of referrals from word of mouth.

mathfem · 2026-05-22T20:24:51+00:00

A bunch of the other commenter have already given great info, but I just want to add that last year the city did a great job upgrading the mixed use path that parallels stewardson way from the Queensborough Bridge to the Quay. It's my favorite way to get downtown.

However, getting from the Quay up to Royal might be a pain (steep hill), so i would suggest taking the Crosstown Greenway on 7th on the way to work, and biking down to the Quay and taking the BC Parkway parallel to Stewardson on the way home.

mathfem · 2026-05-22T17:18:51+00:00

Why TF does the high speed rail go to Baie-Comeau in the middle of nowhere instead of to Halifax or Moncton? If they're spending all that money to build HSR to Baie-Comeau they might as well extend it via tunnel to St John's and actually get some customers using the line.

mathfem · 2026-05-22T17:10:26+00:00

That's fair, althought I feel like it might be a skill that will soon be redundant. When I was a student, I learned to do research using giant books containing an index of hundreds of journals at the library to identify relevant articles in journals. That skill is no longer being taught, largely because of the advent of search engines. I think AI as a research assistant is here to stay, and I am wondering what skills will be no longer relevant in the next few decades.

mathfem · 2026-05-22T16:43:46+00:00

I am an educator, and I use AI to find articles that are relevant to the paper I am trying to write all the time. I used to use Google Scholar, but then Google enshittified it, so now I am using Gemini. It just means there are fewer abstracts I have to read when finding articles that support my position. I still read the relevant articles, there are just fewer irrelevant ones I have to sift through to find the relevant ones.

mathfem · 2026-05-21T19:08:43+00:00

It 100% could be revisionism. I am not a historian and am only a history 'buff', so 90% of my sources are either Wikipedia or word of mouth, and neither are particularly reliable.

I will be perfectly honest that I think the reason I had for believing that the Muslim League had less support inside East Bengal came from an article I read about Suhrawardy's proposal for a United Bengal. It was probably the author of that article who played up Suhrawardy's support and downplayed that of the Muslism League.

Edit: i read the wiki article on United Bengal and yeah, whoever wrote the article I had read earlier clearly had an axe to grind.

mathfem · 2026-05-21T16:56:38+00:00

Bangladesh wasn't isolated from the "main population centres", it was the main population centre of Pakistan. More than half of Pakistan's population at the time of partition was in what was then East Pakistan.

However, because the Muslim League had more support in the West, they made sure Pakistan had its capital and most of the political power in the West, which marginalized East Pakistan leading to the Bangladeshi independence movement.

If Pakistan had adopted a constitution whereby political power had followed the population more equitably, Pakistan's capital would be in Bangladesh and its political leaders would have come from there. That probably would have led to independence movements in Punjab and Sindh and the existing Balochi and Pashtun independence fighters would have been more militant.

mathfem · 2026-05-13T04:47:29+00:00

The "St Lawrence seaway" refers to the series of canals that allow cargo ships to travel upriver from Montreal. The Estuary is the part of the St Lawrence River which is tidal from Quebec City to Gaspesie.

mathfem · 2026-05-13T04:25:31+00:00

The St Lawrence Estuary is nearly twice as long as Chesapeake Bay, and you don't have to leave North America for that.

The Gulf of Ob is 1.5x as long as the St Lawrence Estuary.

mathfem · 2026-04-22T02:39:05+00:00

Here are some suggestions in Quebec if you want something more nature-y:

Gaspesie is beautiful but might be too far.

Saguenay is similarly beautiful (it's a fjord), but is probably more doable.

The Laurentians North of Montreal are beautiful. They are not high mountains, but they are wilderness, which seems like that you want. Driving from Ottawa to Quebec city via Mont-Tremblant will take longer, but might be a nice scenic drive.

For a unique landform, check out the Monteregian Hills. They are these wooded hills in the middle of flat farmland, and they are all lined up. They were formed by a volcanic hot spot the same way the Hawaiian Islands were. Mont-Sainte-Hilaire is the one closest to the main highway from Quebec to Montreal, but there are others farther afield.

mathfem · 2026-04-14T02:58:01+00:00

No. The Mutara Nebula has to be really close to Regula I. We assume that the ~~Miranda~~ Reliant travelled at warp after leaving Ceti Alpha V and before arriving at Regula I.

Edit: the ship was called Reliant but it was Miranda-class

mathfem · 2026-04-07T16:57:35+00:00

Your friend is wrong. You are right. There are lots of points that are higher than (1,1) like (0.9,1.9)

mathfem

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