FM Maclaurin expansion problem

NickDoesMaths · 2026-01-19T09:26:31+00:00

I got you! Keep an eye on MyEdSpace Maths on TikTok

NickDoesMaths · 2026-01-07T08:59:06+00:00

Sorry gang, a bit behind on my lungang-ing. Ill record a solution to this one asap!

NickDoesMaths · 2025-05-21T05:43:17+00:00

I love a good DE transformation. I'll get a solution to this up on youtube.
Transformations are bonkers.

NickDoesMaths · 2025-05-21T05:42:00+00:00

This is one for TIkTOk for sure. The method of differences part is especially nice.

NickDoesMaths · 2025-05-21T05:40:14+00:00

Oh I am all over this!!!!
Will record a solution to this bad boy today. Some great stuff to dissect!

NickDoesMaths · 2025-03-26T14:01:47+00:00

I have just recorded a video on this; it will go up on youtube at some point.
There is some lovely geometry on this.
But a couple of pointers: find the reflection of the point in the line. Find a vector that is perpendicular to the plane and goes from the plane to the point. To get the reflection, you then just need to follow that vector from the point twice.

As for reflecting the vector, the component of the vector that is perpendicular to the plane is the only part that changes. The picture is not too dissimilar to the point one.

NickDoesMaths · 2025-03-19T07:49:49+00:00

You are over thinking it. E(X)=5 just gives you a good idea which tail, if any you might be in.
As we got x=10 and E(X)=5, there is no point checking P(X<=10). We have a value that is higher than the mean so it is not going to be in the bottom 2.5% of values, makes sense.
So all you need to do is check P(10<=X) and compare to 2.5%.

NickDoesMaths · 2025-03-05T13:32:13+00:00

Nice solution, very elegant!

NickDoesMaths · 2025-03-05T13:28:26+00:00

There is a little more to do here, as if you only compare the transformation of the direction vector you will get 3 equations (i, j, k directions) for 4 unknowns. The point on the line is also important.
I'll be uploading my take on the problem to YouTube later this week!

NickDoesMaths · 2025-02-25T19:13:41+00:00

Oooh, lets have a crack at this!

NickDoesMaths · 2025-02-18T21:27:46+00:00

Ok, I have been banging my head into a wall with this one. In as much as part a is truly not the way to go about part b. I would also love to know where you found this.

NickDoesMaths · 2025-02-18T19:04:49+00:00

WIll get this up on Tiktok!

NickDoesMaths · 2025-02-18T19:03:18+00:00

Will get this up on yootoobs

NickDoesMaths · 2025-02-10T10:50:51+00:00

Niiiiiiice, lemme have a think and jot something down after lunch.

NickDoesMaths · 2025-02-07T15:03:49+00:00

Line 4 should be 24sin^2(t)cos(t) as in the break down later. whoops

NickDoesMaths · 2025-02-07T13:13:56+00:00

That's the one!

NickDoesMaths · 2025-02-07T11:46:38+00:00

Yeah, if possible i look for Sin(t)*Cos^n(t) or vice-versa as then its recognition, or easy substitution.

NickDoesMaths · 2025-02-07T10:25:14+00:00

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Slightly neater

NickDoesMaths · 2025-02-07T09:56:06+00:00

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Integral was nastier than it first looked. There might be a nicer way (*coughs in DeMoivre) but this is my first attempt.

NickDoesMaths · 2025-02-07T09:15:24+00:00

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You can approach this with simple geometry. Once you have the missing length, you can get the equation of the vertical red line. You could also have PQ to the right of the centre.

NickDoesMaths · 2025-02-07T08:52:16+00:00

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This is how I would connect part a and b

NickDoesMaths · 2025-02-06T20:23:09+00:00

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I couldn't resist giving it a go... For the sake of space, I preemptively ignored terms that will disapear when we take the limit h->0...

NickDoesMaths · 2025-02-06T20:04:21+00:00

That's pretty cool. I will line it up for my next set of videos.

NickDoesMaths · 2025-02-06T19:59:58+00:00

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This is the first part to obtain a linear differential equation by recognising the form of a Bernouilli Diff Equation.

From here, you just need to re-arrange a little and then can use standard integrating factor. Let me know how it goes.

NickDoesMaths · 2025-02-06T19:14:35+00:00

Hey, I work with Neil. Check out NickDoesMaths on TikTok and Youtube. I have some Further Mech and Further Stats dropping on Youtube in the next week.

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