use calculus, NOT calculators (fast!)

Use calculus, NOT calculators! Here we will use a local linear approximation for sqrt(x) around x=4 to approximate sqrt(4.9). If you use a calculator, then you will see that sqrt(4.9) is about 2.21359..., which shows our approximation is very good!

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bprp #fast

[sgcyt]

That was the fastest tangent line tutorial I have ever seen

[MathAdam]

Method #3: sqrt(4.9) is 0.7 x sqrt 10, which is close to pi. So, 22/7 x 0.7 = 2.2.

[ajmalabidinnur]

I literally thought he was talking in another language.

[bprpfast]

1. Hi!
2. Did you like my instant transmission at 0:00?

[QweRinatrtY]

see when he does the taylor expansion of first order he's showing a cool trick

but when i do it with the sine function at x=0 i'm an engineer

[arijeetnath]

This isn't fast, its too fast
He is just literally rapping.

[nmikk]

This video personifies every single math class I've ever been in. I kind of understand it initially but then it starts derailing to the point that I have no idea what anything means because there is no explanation. I then space out and all of a sudden class is over and I haven't learned a damn thing

[hamyowsker]

This is the teacher everyone records, then watches later at .25 speed

[sarthakvarshney]

Great tutorial!

Alternate approach:
Sqrt(4.9) = sqrt(49/10)
= 7/sqrt(10) = 7/sqrt(9+1)
= 7/(3*sqrt(1+1/9))
~ 7/(3*(1+1/18)
=7/(19/6)
= 42/19

[johnchessant]

22^2 = 484 so sqrt(4.9) = sqrt(490)/10 = about 2.2

In fact you could do sqrt(4.9) = 2.2 + (4.9 - 4.84)/(2 * 2.2) = 2.2 + 0.06/4.4 = 2.2 + avg(0.015, 0.012) = 2.2135
(4 decimal accuracy just by taking the initial point closer to the target)

[reddyprakash]

f ( x + 🔼 x ) = f ( x ) + m 🔼x, ( nearly same ) m = slope at that point, 🔼x = small change in x

[IsaacPrinTheNerd]

According to a Fermi estimate of the answer, given by the proportion of answers in the poll:
2.1(.04) + 2.2(.68) + 2.3(.28) = 2.224
This is within 0.47% the actual answer, and is actually closer than the calculus approximation (off by 0.515%).

[Azkinyte]

this should become a new genre in rap: "math metal"

[-...................-]

when a teacher repeatedly says 'right? right? okay? understood? etc' it just confuses the hell out of me.

[ROCKY_T]

I watch many videos at 2X speed but this is one where I need to slow down.
Great video BTW.

[xxxx]

Taylor expansion is truly savage
Even 2 terms get it done

[datfacepriceless]

I found out while playing in the desmos calculator that
x^(x-1)^(x-2) as it approaches 1 goes to e

just thought I'd share (:

[kimothefungenuis]

We use this technique a lot when linearizing control systems

[bondzy]

That’s was the legitest math flex I have seen, ever.

[Idran]

Another way to do it: look for the square number closest to 490 :P

22^2 = 484, so 2.2^2 = 4.84, so sqrt(4.9) ~= sqrt(4.84) ~= 2.2

That's how I usually ball park a square root to one decimal place :D