Find a root of the equation x^3 4x 9 using Bisection method, correct to three decimal places

Discuss the following:

Significant digits

Round-off errors

2. Find a real root of the equation x using the Newton-Raphson method.

3. Apply Gauss elimination method to solve the following equations:
x 4y z
x y 6z -12
3x y z 4

4. Solve the following equations by Jacobi's iteration method, correct to two decimal places.

10x y z 11.19
x 10y Z 28.08
Y 10z 35.61

5. The table gives the distances in nautical miles of the visible horizon for the given heights in feet above the earth's surface. Using Newton's forward interpolation formula, find the values of y when x 218 feet.

<img src='./qimages/10295-5.jpg'>

6. Find the polynomial by using Lagrangian interpolation formula and hence find for the following:

<img src='./qimages/10295-6.jpg'>

Use Trapezoidal rule to estimate the integral

<img src='./qimages/10295-7a.jpg'>

taking 10 intervals.

Use Simpson's 1/3 rule to find

<img src='./qimages/10295-7b.jpg'>

by taking seven ordinates.

8. Use Runge-Kutta method of fourth order to solve
dy/dx with at x 0·2.

9. Discuss the following:

Constrained Optimisation Problem

Fibonacci Method

Unimodal Functions

Eigen Vectors


10.(a) Discuss the salient features of Golden Section method with suitable example.

Discuss the salient features of unconstrained minimization problems.