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b) Using Newton's forward difference interpolation formula evaluate f(2.05) from the 6
following table
x | 2.0 | 2.1 | 2.2 | 23 | 2.4

f(x)| 1414214 | 1.449138 | 1483240 | 1.516575] 1.549193
5 |

c) Find an approximate value of loges by evaluating f using Simpson's 1/3 8
rule with h=0.5

9 a)The transition probability matrix of a Markov chain { XO, n=1,2,3,....-having 10

0.1 0.5 04 three states 1,2 and 3 is P |
=0.3 0.4 0.3 |
0.60.20.2 |

And the initial distribution is
)ട [9.79.2 0.1 1. FindP(X2=3)

b) Evaluate 11 மட using trapezoidal rule 5
010

௦) Using Runge-Kutta method of order four, find ൮൫.2) given that — = y — x, y(0)=2 5 by
taking h=0. I

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