use calculus, not calculators

Рет қаралды 11,732

Жыл бұрын

Use calculus, not calculators! Tangent line approximation (aka local linear approximation) and differential to approximate the irrational number sqrt(100.5)
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Пікірлер: 40

@neilgerace355 Жыл бұрын

10 ... Didn't use any calculus either :) I think that's the engineer's answer :)

@IamBATMAN13 Жыл бұрын

As a software engineer, I say the answer is 10.0000000023

@SbF6H Жыл бұрын

@@IamBATMAN13 mfw computers are calculators

@oenrn Жыл бұрын

10.0 is a great approximation to 3 significant figures.

@sinpi6332 Жыл бұрын

e * e = 2e = 4

@HappyGardenOfLife Жыл бұрын

@@sinpi6332 e + e = 2e, e * e = e^2, either way everyone knows e = 3.

@aikendrum2908 Жыл бұрын

For people who remember their Taylor series, it is very fast to factor out the 10 and use (1+x)^n ~ 1 + nx where n=1/2 and 1+x = 1.005. You can get 10 * 1.0025 = 10.025 without writing anything down. This also works for other powers, like cube roots, etc., which are of this form, and if you’ve forgotten it, the linear term in the Taylor series (or Maclaurin series if you prefer) is easy to calculate as well.

@johncrwarner Жыл бұрын

(10 + h)^2 = 100.5 100 + 20h + h^2 = 100.5 20h + h^2 = 0.5 h^2 is very small 20h ~ 0.5 h ~ 0.025 => sqrt (100.5) ~ 10.025 I remember doing this as a sort of Newtonian calculus early on in learning the calculus.

@General12th Жыл бұрын

Matt Parker's method!

@johncrwarner Жыл бұрын

@@General12th Like all naming conventions - we tend to associate it with the person we saw it from first or the person our teacher associated it with. In my case Newton in yours Matt Parker.

@michaeledwardharris Жыл бұрын

Very nice. Approximation by linearization makes more intuitive sense to me, but clearly the differential method is way more awesome.

@Dissandou Жыл бұрын

They’re essentially the same

@sriprasadjoshi3036 Жыл бұрын

That intro with "Square root of 100 is NICE number " got me,..

@drawingforyou4626 Жыл бұрын

10.0249 to be more exact Using long division

@Misteribel Жыл бұрын

Next digits are 688 (ie 10.0249882). So 10.0250 is closer to the given approximation than 10.0249. Still cool you used long division though!

@SuperYoonHo Жыл бұрын

Thank you sir! i knew this method from somewhere

@finmat95 Жыл бұрын

4m48s to do something you can do in 4s with calculator.

@carxofa1 Жыл бұрын

My guess before watching: approximating via tangent lines. Let f(x)=√x. We know f(100)=10 because 10^2 = 100. f'(x) = 1/(2√x), f'(100)=1/20=0,05 which is pretty small compared to 100, so: f(100,5)≈f(100)+0,5•0,05 = 10 + 0,025 = 10,025. It should be close enough considering the f(100)/f'(100) ratio is big

@orchestrain88keys Жыл бұрын

Use binomial theorem.. It will be much easier and faster.

@Misteribel Жыл бұрын

If it’s so fast, could you explain how?

@PalaceOfTheFree Жыл бұрын

Ten and a tiny bit. Done

@sidshobha8023 Жыл бұрын

Using calculus gives you better understanding than using calculator...

@txkflier Жыл бұрын

I guessed 10.02 which is 100.4004. So I was within 0.1% using only my brain cells.

@nemesis2022pf Жыл бұрын

It's aproximately 10.

@OnaSoto Жыл бұрын

Do you Americans not get thought the square root extraction algorithm in school? Do they just throw you a calculator for elementary algebra?

@robertcotton8481 Жыл бұрын

American get taught nothing

@Crackkka Жыл бұрын

🤓

@sunset6958 Жыл бұрын

Hmm

@jkid1134 Жыл бұрын

Yeah, not standard at all here in the states. Really weird too because it's very similar to long division, which we do learn. It's the first thing I think of when I see this though. "sure, how many digits you want?" What happened over there (also where?), did they give you an algorithm and a quiz in a week, or did they explain why what you're doing works?

@OnaSoto Жыл бұрын

@@jkid1134 If you have a perfect square, then you’ll get a result part of the natural number set. If you have a square roots that yields you a irrational number, then you can just approximate with 2,3, whatever number of decimals. root 100.5 is very easy to do, I could send you a video of the algorithm we use if you would want.