You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
Approximation of roots using Newton-Raphson method
- Thread starter imnerd
- Start date
Hello, imnerd!
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.
galactus' suggestion is absolutely correct . . .Starting with \(\displaystyle x\,=\,1\) as a 1st approximation,
use Newton-Raphson method to find a second approximation to \(\displaystyle 2^{\frac{1}{20}}\)
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.