If 0·333 is the approximate value of find the absolute, relative and percentage errors.

Find a root of the equation x^3 -4x 9 using the bisection method, correct to two decimal places.

By using the Regula-Falsi method, Find an approximate root of the equation x^4 10 that lies between 1·8 and 2. Carry out three approximations.

Apply Newton-Raphson method to find an approximate root, correct to three decimal places, of the equation x^3 -3x O.

Solve the following system of linear simultaneous algebraic equations by Cramer's rule:

4x1 3x2 6x3 13

2xl -4x2 x3 8

3xl 6x3 17

Given dy/dx= with y=1 for x =0. Find y approximately for x 0·1 by Euler's method (Five steps).

Using bisection method, compute one root of e^X -3x correct to two decimal places.

Find a real root of the equation 0 by Regula-Falsi method in the interval 16) correct to three places of decimal.

Compute the cube root of 20, correct to two decimal places, by using any numerical method.

Solve 3x sin correct to 4 decimal places using the Newton-Raphson method.

Find a real root of the equation e^X -3x 0 by the method of iteration.

Solve the equations

2xl x2 X3 10

3xl 2x2 3x3 18

x1 4x2 9x3 16

using the Gauss elimination method.

Solve the equations

lOx-y-z -33

22

x+y-10z

by Gauss-Jordan method.

Using Runge-Kutta method, find the value of y when x 0.01, given that x 0 when y=1 and dy/dx y^2.

Solve the equations

6x-3y+ z 11



z=10

by Gauss-Seidel method.

Prove the following:



a^2

Use Lagrange's interpolation formula to fit a polynomial to the following data

<img src='./qimages/11459-5b.jpg'>

Also compute

Find

<img src='./qimages/11459-5c.jpg'>

by using Simpson's 1/3 rule. Hence, obtain the approximate value of n.