Question

Using Newton-Raphson method, find a root correct to three decimal places of the equation sinx=1−xsinx=1−x

Select one:

a.

None of these.

b.

0.500

c.

0.555

d.

0.511​

Answer 1

Given : sin x = 1 - x​

To Find : a root correct to three decimal places Using Newton-Raphson method

Solution:

sinx  = 1 - x

=> sinx + x - 1  = 0

f(x) = sinx +  x - 1

f'(x)  = cosx  + 1

x₀  = 0

xₙ₊₁  = xₙ ​−f(xₙ​)​./ f′(xₙ​)

x₁  =  0   - (-1)/2

=>  x₁   = 1/2

x₂ = 0.510958

x₃ = 0.510973  

x₄   =0.510973  

x₅  = 0.510973

correct to three decimal places  = 0.511

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