Question

The equation f(x) is given as x2 – 4 = 0. Considering the

initial approximation at x=6 then the value of next
approximation correct upto 2 decimal

Answer 1

The correct answer is "
`(10)/(3)`".

Step-by-step explanation:

The given function is:

`f(x)=x^2-4=0`

and,

`x_0=6`

By differentiating with the help of Newton's Raphson method, we get

⇒
`x_(n+1)=x_n-(f(x_n))/(f'(x_n))`

then,

⇒
`x_1=x_0-(f(x_0))/(f'(x_0))`

`=6-(f(6))/(f'(6))`

`=6-((6)^2-4)/(2* 6)`

`=6-(8)/(3)`

`=(10)/(3)`