11.

12.

18.

14.

15.

16.

11

18.

19.

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2 D 10668

Write Newton’s Forward difference formula.
Set up Newton-Raphson formula for computing «सि.

(8 x 3 = 24 marks)
Section B

Answer at least five questions.

Each question carries 5 marks.

All questions can be attended.
Overall Ceiling 25.

Find a root of f (x) = x?— 3x —5 = O correct to 3 decimal places using Newton-Raphson method. Start
with x, =3
0= 3.

Using Lagrange’s interpolation formula find y (10) 17:
2 : 5 6 9 11
೫ :; 12 13 14 16

Using Newton’s forward interpolation formula find the cubic polynomial for the data :
൬: 0 1 2 3

y 3 1 2 1 10
١ 21 6 ۱ 3 .
Approximate |, = dx using Simpson’s 8 th rule with step value A = 0.25
Using Second derivative midpoint formula approximate f!! (1.3) if f (x) = 3xe*— cos x with h = 0.1.
Given :
೫% 1.9 1.29 1.30 1.31 1.40
y: 11.59006 13.78176 14.04276 14.30741 16.86187

Use Euler’s method to find approximate solution for the initial value problem y! =1 ಜತೆ

9

1 < £ < 2,y () =2 withh =0.25.

Use Newton’s Backward difference formula to construct interpolating polynomial of degree 1 if

f (— 0.75) = —.07181250, f (— 0.5) = —.02475000, f (—.25) =.33493750, f (0) = 1.10100000.

(5 x 5 = 25 marks)

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