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23 Maths -- Numerical Computations

The general formula of solving a non-linear equation of f(x)=0 by Newton Raphson method is:a. x n =x n+1 -f(x n )/f'(x n )b.x  n+1=x n -f(x n )/f'(x n )c.x n =x n+1 -f(x 0 )/f'(x 0 )d.x  n+1=x n -f"(x n )/f(x n )

The general formula of solving a non-linear equation of f(x)=0 by Newton Raphson method is:

a. x n =x n+1 -f(x n )/f'(x n )

b.x  n+1=x n -f(x n )/f'(x n )

c.x n =x n+1 -f(x 0 )/f'(x 0 )

d.x  n+1=x n -f"(x n )/f(x n )

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Applying the method of successive bisection find square root of 3 within the two places of decimal in (1,2)

Using bisection method, find the root of the equation f(x)=x2 -6logx-3=0(2<=x<=3)'correct to 4 decimal places with an accuracy of 10 -2 .

Here, f(x)=x2 -6 logx-3=0

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Now

n
 a(-ve)
 b(+ve)
 cn
 f(cn)
0
 2
 3
 2.5
 0.8623
1
 2
 2.5
 2.25
 -0.050595
2
 2.25
 2.5
 2.375
 0.38664
3
 2.25
 2.375
 2.3125
 0.1631658
4
 2.25
 2.3125
 2.28125
 0.05506
5
 2.25
 2.28125
 2.265625
 0.001925

From the table,

f(2.265625)=0.001928<10-2

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