use local linear approximation, no calculator!

Approximating cbrt(1001) by using calculus, no calculators!

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#justcalculus

[DeJay]

"Approximate cbrt(1001) up to 2 decimal digits"

Sure: 10.00

[dimitris]

I'm an engineer and answer is π^2

[rahenson]

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]

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 +

Multiply by 10
= 10 +

Approximated value:
Actual value of cbrt 1001 = 10.0033322228

Very close!

[yamikira]

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

[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.

[zayedalsuwaidi]

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?

[moeberry]

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

[NoNameAtAll]

wait, did RedpenBlackpen change name?

[tubax]

Just use a calculator bro it's 10.00333