or
Close Menu

23 Maths -- Numerical Computations

Using Newton-Raphson method, find a root off(x)=sinx+x-1=0 in (0,1)

Using Newton-Raphson method, find a root of

f(x)=sinx+x-1=0 in (0,1)

0 Answers

1067 Views

More questions on Numerical Computations

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

f(2)=4-6 log2-3=-0.806

f(3)=9-6 log3-3=3.1373

f(2).f(3)=-0.806*3.1373=-2.529422 which is negative.

Hence, the root lies between 2 and 3

c0 =(2+3)/2=2.5

f(2.5)=6.25-6 log 2.5-3=0.8623

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 

...

Which one of the following is transcendal equation? ax 2 +2hxy+by2 =0 2x3 +4x+5=0 4x+5y=10 xex -1=0

4.xex -1=0

The characteristics of the computational method is accuracy rate of convergence numerical stability all of the above

Use Newton-Raphson method to find the root off(x)=x 3 -9x+2=0 with accuracy of 10 -3 .

Show that the equation f(x)=2x 3 -5x+2=0 has one negative root and one positive root between 1 and 2. Using method of bisection, find a positive root of the equation with error less than 10 -1 .

If f(0)=-1 and f(8)=1, how many iterations of bisection of the interval will be required to find an approximation to the root of f(x) accurate to 0.25?

One root of the equation ex−3x2=0 lies in the interval(3,4). Find the least number of iterations of the bisection method, so that error is less than 10 -3

Use Newton's Raphson method to find the cube roots of 4 correct to 4 places of decimals with error less than 10 -5

The first iteration root of the equation f(x)=x 2 -5=0 when initial guess value is 2 is :a. 2.25b. 2.20c. 2.10d. 2.32

For a continuous function f(x) on (a,b) the equation f(x)=0 has at least a root in between a and b if a. f(a)f(b)=0b. f(a)f(b)<0c. f(a)f(b)>0d. None of them

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&nbsp; n+1=x n -f(x n )/f'(x n )c.x n =x n+1 -f(x 0 )/f'(x 0 )d.x&nbsp; ...

For a continuous function f(x) on (a,b) the equation f(x)=0 has at least a root in between a and b if a. f(a)f(b)=0b. f(a)f(b)<0c. f(a)f(b)>0d. None of them

Close Open App