use local linear approximation, no calculator!
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- čas přidán 4. 04. 2022
- 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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"Approximate cbrt(1001) up to 2 decimal digits"
Sure: 10.00
I'm an engineer and answer is π^2
WHAT
You mean pi^2
@@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
@@navra3173 you mean that g=π²=e²
No 10(g) is not equal to 9(pi^2) is not equal to 4(e^2)
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.
End made my smile. Instead of just ignoring x-1000 we go through half as many steps as entire calculation.
I LOVE THIS GIY
Thank you
Make a function f(x)=x^3-1001 and use Newton's Method
😆
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.
Easier to differentiate
3 take it or leave it
3? Do you mean 10?
@@oliverolsen1120 3
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!
i like it
Cool!
Got to learn something new :)
thx lord
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.
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…
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)
2:33 when you rewrote x to the power of -2/3 isn’t it supposed to be the cube root of the square of 1000?
Instead of the square of the cube root of 1000
taylor development 🤪i love it
10
Minisculely greater than 10
Better use binomial approximation
The differential form is easier to me
wait, did RedpenBlackpen change name?
oh, it just doesn't have bprp listed in Channels section...
This was not needed this is already so close to 10 at 2 decimal places.
Or just use a calculator
No it's no fun 😊
Just use a calculator bro it's 10.00333
hes trying to teach calculus not how to use a calculator
10