use local linear approximation, no calculator!

Рет қаралды 23,052

2 жыл бұрын

Approximating cbrt(1001) by using calculus, no calculators!
Check out how to use Newton's Method to approximate an irrational number: • approximate 4th root o...
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Пікірлер: 43

@DeJay7 2 жыл бұрын

"Approximate cbrt(1001) up to 2 decimal digits" Sure: 10.00

@dimitris17 2 жыл бұрын

I'm an engineer and answer is π^2

@hata6290 2 жыл бұрын

WHAT

@two697 2 жыл бұрын

You mean pi^2

@navra3173 2 жыл бұрын

@@hata6290 pi squared is equal to 9.8 ≈10 ( which is also equal to acceleration due to gravity of earth ) Conclusion, g ≈ pi^2 ≈ 10

@dimitris17 2 жыл бұрын

@@navra3173 you mean that g=π²=e²

@midnightgamer4201 2 жыл бұрын

No 10(g) is not equal to 9(pi^2) is not equal to 4(e^2)

@rahenson1 2 жыл бұрын

Once you have the formula seems it would have been easier to leave the 1/300 outside than distribute. Plug in 1001 for x and you just have 10 + (1/300) * 1 or 10 and 1/300.

@MsBombastik 2 жыл бұрын

End made my smile. Instead of just ignoring x-1000 we go through half as many steps as entire calculation.

@AnakinSkywalker-zq6lm 2 жыл бұрын

3 take it or leave it

@oliverolsen1120 2 жыл бұрын

3? Do you mean 10?

@AnakinSkywalker-zq6lm 2 жыл бұрын

@@oliverolsen1120 3

@hata6290 2 жыл бұрын

I LOVE THIS GIY

@yamikira6512 2 жыл бұрын

Make a function f(x)=x^3-1001 and use Newton's Method

@bprpcalculusbasics 2 жыл бұрын

😆

@givrally7634 2 жыл бұрын

Well, you do get 10+1/300, which is the same answer linearization gets you. Wait no actually this makes sense since Newton's method is basically just linearization but in reverse. Instead of saying "I know this function's value at a nearby point and I want to approximate the value at my point of interest" you say "I want to find what my point of interest is, and I know a point that's very close to it". Instead of knowing the y values and working with that, you know the x values and you work with that. So yeah it makes sense after all.

@vizart2045 Жыл бұрын

Easier to differentiate

@goblinthebuble 4 ай бұрын

Thank you

@itsphoenixingtime 2 жыл бұрын

Binomial expand (1+x)^n with n as 1/3, x = 0.001, then multiply the result by 10. since cbrt1001 = cbrt1000 * cbrt 1.001 = 10 cbrt 1.001 lets try it! (1+x)^n = 1 + nx + n(n-1)/2 x^2 + ..... (since x = 0.001 it will be very small, we can just use up to the 2nd power 1 + 1/3 (0.001) + (1/3)(1/3 - 1)/2 (0.001)^2 + ....... 1 + 1/3000 - 1/9000000 = 1 + 2999/9000000 Multiply by 10 = 10 + 2999/900000 Approximated value: 10.0033322222.... Actual value of cbrt 1001 = 10.0033322228 Very close!

@orngng 2 жыл бұрын

i like it

@Pankaw 2 жыл бұрын

Cool!

@aasthaiitbombae5750 2 жыл бұрын

Got to learn something new :)

@Can-hb6ls 2 ай бұрын

thx lord

@fanigamotoqueiro502 2 жыл бұрын

@matteocilla9482 2 жыл бұрын

taylor development 🤪i love it

@chitlitlah 2 жыл бұрын

The result on the left is still hard to convert to decimal without a calculator. It seems like a wasted effort to me. The one on the right is reasonable if you somehow find yourself without a calculator and need a closer estimate than just 10.

@ieatgarbage8771 2 жыл бұрын

No one’s actually doing this because they need it lol but if you want 1001/300+20/3 3001/300 10+1/300 10.00333…

@rubenverg 2 жыл бұрын

you can just ignore the last steps, back when you have 10 + (x-1000)/300 just plug in x = 1001 and get 10 + 1/300, which is quite obviously 10.00(3)