If 0·667 is the approximate value of 2/3,find the absolute, relative, and percentage errors.

Using bisection method, find a real root of the equation x^3 5x 1 correct to two decimal places.

Find the root of the equation xe^x cos x using the Regula-Falsi method, correct to four decimal places.

Apply Newton-Raphson method to find an approximate root, correct to three decimal places, of the equation x sin x 0

By the fixed point iteration process, find the root, correct to three decimal places, of the equation x cos x near .

Solve the following set of simultaneous equations by Cramer's rule

x1 2x2 — 3x3 — 4

2x1 — 3x2 x3 1

3x1 — 5x2 4x3 5

Find the root of the equation e^x x 2 using bisection method, correct to three decimal places.

By using the Regula-Falsi method find the root, correct to three decimal places, of the following equation over the indicated interval

xe^x 3 over

Find the cube root of correct to three decimal places, by using any suitable numerical method.

Using Newton-Raphson method, find the real root of the equation x tan x 1·28, correct to three decimal places.

Solve the following algebraic equations by using Gauss' elimination method:

x y z 6

3x 3y 4z 20

2x Y 3z 13

Solve the following simultaneous equations by using Gauss-Jordan method

5x -2y 3z 18

x 7y -3z -22

2x y 6z 22

Solve the following simultaneous equations

x y z 3

2x y 3z 16

3x z

Use Jacobi's iteration method to solve the following system of equations

20x y 2z 17

3x 20y -18

2x 3y 20z 25

Solve dy/dt y^2 given boundary conditions y l at t 0. Find approximately the value of y for t 1 by Euler's method in five steps.

Prove that

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"Use Lagrange's interpolation formula to compute from the given data:

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Use Runge-Kutta method to aproximate whenx 0·1 and x 0·2,given that x when y 1 and dy/dx x y.