Question

Find the real root of the equation 3x-cosx-1=0 correct to four decimal places using the Newton Raphson Method.

Answer 1

let y = 3x - cosx - 1
y' = 3 + sinx

newx = oldx - (3oldx - cos(oldx) - 1)/(3 + sin(oldx))
let's take a look
http://www.wolframalpha.com/input/?i=plot+y+%3D+3x-cosx-1
it appears x = .5 could be a good start
x ..... newx
.5 ---- .6085..
.6085 .60710
.60710 .60710 <---- same result correct to 5 decimals

check in original:
LS = 3(.60710) - cos(60710) - 1
= -.0000058... , not bad

Answer 2

 Find a real root of the equation x3 – x – 1 = 0 using Newton - Raphson method, correct to four decimal places.