use local linear approximation, no calculator!

[@DeJay7]

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

[@rahenson1]

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.

[@dimitris17]

I'm an engineer and answer is π^2

[@hata6290]

WHAT

[@two697]

You mean pi^2

[@navra3173]

@@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]

@@navra3173 you mean that g=π²=e²

[@midnightgamer4201]

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

[@MsBombastik]

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

[@itsphoenixingtime]

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]

i like it

[@Pankaw]

Cool!

[@yamikira6512]

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

[@bprpcalculusbasics]

😆

[@givrally]

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]

Easier to differentiate

[@AnakinSkywalker-zq6lm]

3 take it or leave it

[@oliverolsen1120]

3? Do you mean 10?

[@AnakinSkywalker-zq6lm]

@@oliverolsen1120 3

[@zayedalsuwaidi7697]

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?

[@zayedalsuwaidi7697]

Instead of the square of the cube root of 1000

[@HeckYeahRyan]

the square of the cube root and the cube root of the square are the same because (a^b)^c = a^(bc) and a^(bc) can be written as (a^c)^b

[@chitlitlah]

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]

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]

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)

[@goblinthebuble]

Thank you

[@Can-hb6ls]

thx lord

[@hata6290]

I LOVE THIS GIY

[@fanigamotoqueiro502]

10

[@aasthaiitbombae5750]

Got to learn something new :)

[@matteocilla9482]

taylor development 🤪i love it

[@sahilmengji5687]

Better use binomial approximation

[@SJrad]

Minisculely greater than 10

[@arcturusgd]

The differential form is easier to me

[@NoNameAtAll2]

wait, did RedpenBlackpen change name?

[@NoNameAtAll2]

oh, it just doesn't have bprp listed in Channels section...

[@norman4628]

Or just use a calculator

[@jase4066]

No it's no fun 😊

[@moeberry8226]

This was not needed this is already so close to 10 at 2 decimal places.

[@1tubax]

Just use a calculator bro it's 10.00333

[@radiationgaming889]

hes trying to teach calculus not how to use a calculator

[@williamhewitt4748]

10