Approximation of roots using Newton-Raphson method

[imnerd]

i have a question here

Starting with x=1 as a 1st approximation, use Newton-Raphson method to find a second approximation to 2^(1/20).

the equation is not given here, so how to find the second approximation to
2^(1/20)?

plz help me! THX!

 

[galactus]

Try using $\displaystyle x^{20}-2$

 

[imnerd]

what is that?

 

[soroban]

Hello, imnerd!

Starting with $\displaystyle x\,=\,1$ as a 1st approximation,
use Newton-Raphson method to find a second approximation to $\displaystyle 2^{\frac{1}{20}}$

galactus' suggestion is absolutely correct . . .

Let: $\displaystyle 2^{\frac{1}{20}}\,=\,x\;\;\Rightarrow\;\;2\,=\,x^{20}$

. . Then: $\displaystyle \:x^{20}\,-\,2\:=\:0$

And we want a zero of the function: $\displaystyle f(x)\:=\:x^{20}\,-\,2\;\;$ . . . got it?

Now apply Newton-Raphson to this function.