Homework SourseUse NewtonRaphson method to solve fx2x5lnx0 x061 Your approx
Use Newton-Raphson method to solve
f(x)=2x5+lnx=0, x?[0.6,1].
Your approximate solution should be correct up to 5 decimal places.
Does the interval [0.6,1] contain a root of f(x)=0? Y/N
Set up a stopping criterion as follows f(n) error=lZn-z.ISTm)!Solution
Given that f(xn) = 2xn5 + Inxn
Hence, f\'(xn) = 10xn4 + 1/xn
We know that in Newton-Raphson method,
xn+1 = xn - f(xn)/f\'(xn)
= xn - 2xn5 + Inxn/ [ 10xn4 + 1/xn]
xn+1 = xn - 2xn5 + Inxn/ [ 10xn4 + 1/xn]
Therefore,
g(xn) = xn - [ 2xn5 + Inxn ]/ [ 10xn4 + 1/xn]
Hence,
ans = C
![Use Newton-Raphson method to solve f(x)=2x5+lnx=0, x?[0.6,1]. Your approximate solution should be correct up to 5 decimal places. Does the interval [0.6,1] cont](/WebImages/25/use-newtonraphson-method-to-solve-fx2x5lnx0-x061-your-approx-1063278-1761555779-0.webp "Use Newton-Raphson method to solve f(x)=2x5+lnx=0, x?[0.6,1]. Your approximate solution should be correct up to 5 decimal places. Does the interval [0.6,1] cont")
