2. Find Solution using Newton's Divided Difference Interpolation formula

x	f(x)
2	0.69315
2.5	0.91629
3	1.09861

x = 2.7

Solution:
The value of table for `x` and `y`

x	2	2.5	3
y	0.6932	0.9163	1.0986

Numerical divided differences method to find solution

Newton's divided difference table is

x	y	`1^(st)` order	`2^(nd)` order
2	0.6932
		`(0.9163-0.6932)/(2.5-2)=0.4463`
2.5	0.9163		`(0.3646-0.4463)/(3-2)=-0.0816`
		`(1.0986-0.9163)/(3-2.5)=0.3646`
3	1.0986

The value of `x` at you want to find the `f(x) : x = 2.7`

Newton's divided difference interpolation formula is
`f(x)=y_0 +(x-x_0) f[x_0, x_1]+(x-x_0)(x-x_1) f[x_0, x_1, x_2]`

`y(2.7) = 0.6932 + (2.7 -2) xx 0.4463 + (2.7 -2)(2.7 -2.5) xx -0.0816`

`y(2.7) = 0.6932 + (0.7) xx 0.4463 + (0.7)(0.2) xx -0.0816`

`y(2.7) = 0.6932 +0.3124 -0.0114`

`y(2.7) = 0.9941`


Solution of divided difference interpolation method `y(2.7) = 0.9941`

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